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REVIEW 2 major objections 3 minor 167 references

Enhancing Entanglement Purification with Shared Randomness

T0 review · 2 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read The paper claims that accumulating entanglement distribution rounds and shuffling the stored pairs with shared randomness provably improves the success probability and success-weighted output Bell fidelity of any n-to-1 bilocal Clifford EPP

desk verdict Genuine general theorem for AS enhancement of biCEPs, but the abstract overclaims relative to the symmetrized baseline and ideal memories; referee it, ask for qualification. read the letter →

arxiv 2607.21555 v1 pith:OU2BZNJK submitted 2026-07-23 quant-ph

Allen Zang , Bikun Li , Xinan Chen , Eric Chitambar , Liang Jiang , Martin Suchara , Tian Zhong This is my paper · ORCID
classification quant-ph PACS 03.67.-a03.67.Pp
keywords entanglementpurificationsharedrandomnessWernerstatesbilocalCliffordprotocolsquantumnetworkssymmetrizationmajorizationmemories
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that a simple, resource-cheap preprocessing step—accumulating entangled pairs over several distribution rounds and then using shared randomness to shuffle them before feeding the packages to an entanglement purification protocol—provably improves purification whenever the sources are Werner-type and the protocol is a bilocal Clifford EPP. The improvement holds even though the purification layer cannot tell which source produced which pair, and it requires no state characterization or circuit redesign. If true, this gives quantum-network operators a drop-in enhancement for heterogeneous networks: higher expected success probability and higher success-weighted output fidelity, with gains that grow monotonically as more rounds are accumulated.

What carries the argument

The central object is the effective single-package state after accumulating and shuffling (Theorem 1), together with the stabilizer-code interpretation of bilocal Clifford EPPs, which expresses success probability and success-weighted output fidelity as averages of bilocal Pauli correlations. For Werner inputs these become multi-affine polynomials in the visibilities with non-negative coefficients; the proof that AS helps reduces to the elementary symmetric mean inequality e_r(w^{(m)})/C(mn,r) ≥ e_r(w)/C(n,r), obtained via Maclaurin's inequality and Vandermonde's identity, with Schur–Ostrowski majorization handling the asymptotic case.

What would settle it

A numerical search over all stabilizer codes of small n and all visibility vectors w∈[0,1]^n for a biCEP where the finite-m AS expression p_succ(ρ_eff^(m)) is strictly less than the uniformly-random baseline p_succ,noAS would directly contradict Theorem 4; the paper asserts no such case exists. Alternatively, an experiment with two Werner sources at F1=0.5, F2=1 using the bilocal CNOT protocol should show the asymptotic success-probability difference rising to 1/18.

Watch

Extended reading notes

Core claim

For any n Werner sources and any fixed n-to-1 bilocal Clifford EPP, accumulating m copies of each source state, uniformly shuffling all mn pairs with shared randomness, and parceling them into n-pair packages improves both the expected success probability and the success-weighted output Bell fidelity relative to the uniformly-random-label baseline, for every finite m and in the limit m→∞, with monotonic improvement in m (Theorem 4). The mechanism is symmetrization: the effective one-package state becomes a convex mixture whose asymptotic form is the tensor product of the average input state, and the protocol figures of merit, being multi-affine polynomials with non-negative coefficients in t

Load-bearing premise

The theorem compares AS against a baseline in which the unlabeled inputs arrive in a uniformly random source-label permutation; if in practice the ordering is fixed or adversarial, or if the buffer memories decohere above a modest rate, the guaranteed improvement can disappear.

Editorial extensions

If this is right

  • Quantum networks with heterogeneous, unlabeled sources can improve purification using only buffer memories and pre-shared classical randomness, without benchmarking or optimizing the EPP.
  • The improvement is guaranteed for every number of sources n and every bilocal Clifford EPP, so it applies broadly to stabilizer-based purification circuits.
  • Gains increase monotonically with the number of accumulated rounds in the ideal-memory limit, so longer accumulation (when memory permits) is always beneficial.
  • The strategy also works when each source's output is random rather than fixed, as long as the per-source mean states are used in the analysis.
  • Under memory decoherence there is a threshold: for two sources with the standard CNOT protocol, AS can underperform once depolarization per round exceeds r≈0.206 (success probability), so practical deployment should bound accumulation depth.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The symmetrization argument likely extends beyond Werner inputs and Clifford protocols to any protocol whose figures of merit are Schur-concave polynomials in state parameters, suggesting a broader design principle: randomization can convert heterogeneous inputs into more favorable average inputs.
  • The monotonicity in m suggests a resource-theoretic tradeoff: classical randomness and memory time are convertible into purification performance, and the shared-randomness cost might be reduced by derandomizing the shuffle with pseudorandom sequences.
  • The identified thresholds where AS fails under decoherence suggest that, for finite memory quality, there is an optimal accumulation depth m* that could be precomputed from memory error rates.
  • AS could be combined with existing source-characterization tools: even a crude estimate of the average state could guide the choice of which fixed EPP to run, with AS then guaranteeing the average-input performance.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper introduces an "accumulating and shuffling" (AS) strategy for entanglement purification when source labels are unavailable. Alice and Bob buffer m rounds of n distributed pairs, use shared randomness to apply the same random permutation to all mn local memories, and partition them into m packages of size n, each fed to a fixed n-to-1 bilocal Clifford EPP. For n Werner sources with visibilities in [0,1], the paper proves (Theorem 4) that the expected per-package success probability and success-weighted output Bell fidelity are no smaller under AS than under a no-AS baseline defined as the uniform mixture over source-label permutations (Eq. (1)), for every finite m and asymptotically, with monotonicity in m. The proof uses a stabilizer-code reformulation of biCEPs, expresses the figures of merit as nonnegative combinations of elementary symmetric polynomials of the visibilities, and applies Maclaurin's inequality and Vandermonde's identity for finite m and Schur-concavity in the asymptotic limit. The paper also gives explicit DEJMPS two-source results, extensions to general Bell-diagonal inputs, and a threshold analysis of memory depolarization (Proposition 7).

Significance. The mathematical core is rigorous and self-contained: the finite-m reduction to elementary symmetric means and the monotonicity proof are careful, the stabilizer interpretation is sound, and there are no fitted parameters. The paper is also honest about limitations that it does prove, notably that normalized output fidelity is not universally improved (the [[5,1,3]] example) and that memory depolarization above stated thresholds destroys the advantage. If the uniform-permutation baseline is accepted as the correct operational model of label unavailability, the result is a striking and resource-cheap enhancement that is independent of the state parameters and does not require EPP optimization. The main caveat is that this baseline is a modeling assumption, not a consequence of label unavailability; the central theorem does not cover a fixed unknown source ordering. That caveat is the main obstacle to the paper's significance as currently worded.

major comments (2)
  1. [Operational model, Eq. (1); Theorem 4; abstract] The theorem is proven only for the uniform source-label permutation baseline ρ_noAS. The abstract's unqualified 'over the baseline without AS' is broader. If the purification layer receives a fixed but unknown ordering, the no-AS performance can be higher than AS. Example: n=3, biCEP with S=⟨Z1,Z2⟩, w=(1,0.5,0). Fixed-order p_succ=(1/4)(1+w1+w2+w1w2)=0.75, while asymptotic AS gives (1/4)(1+0.5+0.5+0.25)=0.5625. Thus AS is worse than a deterministic no-AS run. The End Matter's appeal to ignorance does not imply a uniform distribution over orderings. The abstract and Theorem 4 should state explicitly that the comparison is relative to the symmetrized no-AS baseline, and the practical scope should be discussed.
  2. [Operational model, Eq. (1)] The no-AS baseline, if implemented as a physical protocol rather than a mathematical average, requires the same classical shared randomness that AS uses: Alice and Bob must agree on a random permutation of the n pairs in each round. If shared randomness is the resource whose benefit is being demonstrated, comparing AS against a baseline that already consumes that resource complicates the resource-theoretic interpretation. If Eq. (1) is instead meant as an ignorance prior, the paper should say so explicitly and avoid implying that shared randomness alone creates the enhancement.
minor comments (3)
  1. [Abstract and Conclusion] Theorem 4 assumes ideal buffer memories. The abstract and conclusion should state this and point to Proposition 7, which gives thresholds r≈0.206 (p_succ), r≈0.106 (F_succ), and r≈0.150 (p_succF_succ) above which AS is worse under memory depolarization.
  2. [Introduction] Typo: 'Werner souces' should be 'Werner sources'. Also, the phrase 'the successful output fidelity' in the End Matter is sometimes used where 'the success-weighted output fidelity' is meant; the distinction is important and should be kept consistent.
  3. [End Matter / Section V] The memory-decoherence discussion is transparent, but it would help to state explicitly in the main text that the no-AS baseline in the decoherence comparison is the fixed-order baseline (as in Proposition 7), not the uniform-permutation baseline of Eq. (1), to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Theorem 4 is a self-contained inequality proof against an explicitly stated uniform-permutation baseline; self-citations are non-central.

full rationale

The central derivation chain is self-contained. The effective package state is derived from hypergeometric sampling without replacement (Theorem 1, Eq. (2)); the biCEP figures of merit are derived from the stabilizer-code interpretation (Eqs. (7)-(10)); and Theorem 4 is proved by expressing the symmetrized figures as non-negative combinations of elementary symmetric polynomials and applying Schur-Ostrowski, Maclaurin, and Vandermonde inequalities. No parameter is fitted to the predicted quantity: the visibility vector w is an input, not a fitted constant. The no-AS baseline is explicitly defined as the uniform source-label permutation in Eq. (1), and the theorem's statement is exactly a comparison against that baseline; whether that baseline is the right operational model for a fixed unknown ordering is a modeling question, not a circular reduction. The paper even flags where the guarantee fails: normalized successful fidelity is not universally improved, and memory decoherence reverses the advantage above stated thresholds (Proposition 7). Self-citations [13,15] provide context and a memory-decoherence model for a robustness analysis, but are not load-bearing for the guaranteed-enhancement theorem; removing them would not change the proof. No self-definitional, fitted-input-called-prediction, or ansatz-smuggling step was found.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The paper introduces no free parameters or new physical entities. The AS strategy is a protocol primitive, not an entity. The main assumptions are the operational baseline model, the Werner-source restriction, ideal memories in the central theorem, and standard mathematical inequalities.

assumptions (7)
  • domain assumption No-AS baseline is the uniform random source-label permutation (Eq. 1).
    The comparison target is the symmetrized average over all permutations. This is justified by label unavailability, but a fixed-unknown-ordering baseline is also plausible and would break the guaranteed improvement.
  • domain assumption Input states are Werner states with Bell fidelity in [1/2,1].
    The central Theorem 4 is restricted to Werner sources, parameterized by visibility w_i=(4F_i-1)/3.
  • domain assumption Buffer memories are ideal in the main theorem (no idling decoherence).
    Memory decoherence is added later in the End Matter; Proposition 7 shows AS can be worse above depolarization thresholds.
  • domain assumption The EPP is an n-to-1 bilocal Clifford protocol (biCEP).
    The theorem applies to this protocol family, defined by Alice applying U and Bob U^* followed by computational-basis parity checks.
  • domain assumption Multivariate hypergeometric sampling model for AS packages.
    Theorem 1 assumes the shuffle is uniform and packages are formed by sampling n pairs without replacement from the mn accumulated pairs.
  • standard math Maclaurin's inequality, Vandermonde's identity, and Schur-Ostrowski criterion.
    Used to compare elementary symmetric means in Lemma 15 and to establish Schur-concavity in Theorem 14.
  • standard math Stabilizer-code interpretation of biCEP acceptance.
    Success iff Pauli error is in the normalizer N(S_U); output target iff error is in the stabilizer S_U; this gives Eqs. (9)-(10).

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Pith. "Pith review of Enhancing Entanglement Purification with Shared Randomness." pith.science (2026). https://pith.science/paper/OU2BZNJK

@misc{pith2026260721555,
  author       = {Pith},
  title        = {Pith review of: Enhancing Entanglement Purification with Shared Randomness},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OU2BZNJK}},
  note         = {Machine review of arXiv:2607.21555}
}
abstract

Entanglement purification protocols (EPPs) are essential for improving entanglement fidelity to support fault-tolerant distributed quantum information processing. Practical entanglement sources are often heterogeneous and source labels may be unavailable at the EPP layer. We show that classical shared randomness, together with buffer memories, can enhance entanglement purification when source labels are unavailable, without state characterization or EPP circuit optimization. The strategy is to accumulate multiple entanglement distribution rounds and then use shared randomness to shuffle all the stored entangled states before packaging them as inputs to the EPP. For any $n$ Werner sources and any fixed $n$-to-1 bilocal Clifford EPP, we prove that accumulating and shuffling improves the expected success probability and the success-weighted output Bell fidelity over the baseline without accumulating and shuffling, for every $n$, for every finite number of accumulation rounds and in the asymptotic limit, and the improvement increases monotonically with the number of accumulation rounds.

Figures

Figures reproduced from arXiv: 2607.21555 by the authors.

Figure 1
Figure 1. FIG. 1. Two-source schematic of accumulating and shuffling. (a) Alice and Bob receive one pair from each of two non-identical sources in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Difference between [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Difference between [PITH_FULL_IMAGE:figures/full_fig_p032_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

167 extracted references · 4 linked inside Pith

  1. [1]

    Nature , volume=

    The quantum internet , author=. Nature , volume=. 2008 , publisher=

    2008

  2. [2]

    Science , volume=

    Quantum internet: A vision for the road ahead , author=. Science , volume=. 2018 , publisher=

    2018

  3. [3]

    Physical Review Letters , volume=

    Quantum privacy amplification and the security of quantum cryptography over noisy channels , author=. Physical Review Letters , volume=. 1996 , publisher=

    1996

  4. [4]

    Physical Review Letters , volume=

    Purification of noisy entanglement and faithful teleportation via noisy channels , author=. Physical Review Letters , volume=. 1996 , publisher=

    1996

  5. [5]

    Physical Review A , volume=

    Mixed-state entanglement and quantum error correction , author=. Physical Review A , volume=. 1996 , publisher=

    1996

  6. [6]

    Scientific Reports , volume=

    Optimal architectures for long distance quantum communication , author=. Scientific Reports , volume=. 2016 , publisher=

    2016

  7. [7]

    Reviews of Modern Physics , volume=

    Quantum repeaters: From quantum networks to the quantum internet , author=. Reviews of Modern Physics , volume=. 2023 , publisher=

    2023

  8. [8]

    Physical Review A , volume=

    Quantum repeater with encoding , author=. Physical Review A , volume=. 2009 , publisher=

    2009

Show all 167 references
  1. [9]

    Reports on Progress in Physics , volume=

    Entanglement purification and quantum error correction , author=. Reports on Progress in Physics , volume=. 2007 , publisher=

    2007

  2. [10]

    Nature , volume=

    Entanglement purification for quantum communication , author=. Nature , volume=. 2001 , publisher=

    2001

  3. [11]

    Nature , volume=

    Experimental entanglement purification of arbitrary unknown states , author=. Nature , volume=. 2003 , publisher=

    2003

  4. [12]

    Physical Review Letters , volume=

    Long-distance entanglement purification for quantum communication , author=. Physical Review Letters , volume=. 2021 , publisher=

    2021

  5. [13]

    Physical Review Letters , volume=

    Experimental single-copy entanglement distillation , author=. Physical Review Letters , volume=. 2021 , publisher=

    2021

  6. [14]

    Nature , volume=

    Experimental purification of two-atom entanglement , author=. Nature , volume=. 2006 , publisher=

    2006

  7. [15]

    Science , volume=

    Entanglement distillation between solid-state quantum network nodes , author=. Science , volume=. 2017 , publisher=

    2017

  8. [16]

    Physical Review Letters , volume=

    Entanglement purification and protection in a superconducting quantum network , author=. Physical Review Letters , volume=. 2022 , publisher=

    2022

  9. [17]

    Physical Review A , volume=

    Optimizing practical entanglement distillation , author=. Physical Review A , volume=. 2018 , publisher=

    2018

  10. [18]

    Quantum , volume=

    Optimized entanglement purification , author=. Quantum , volume=. 2019 , publisher=

    2019

  11. [19]

    npj Quantum Information , volume=

    Qubit metrology for building a fault-tolerant quantum computer , author=. npj Quantum Information , volume=. 2015 , publisher=

    2015

  12. [20]

    Nature Physics , volume=

    Efficient learning of quantum noise , author=. Nature Physics , volume=. 2020 , publisher=

    2020

  13. [21]

    Nature Reviews Physics , volume=

    Quantum certification and benchmarking , author=. Nature Reviews Physics , volume=. 2020 , publisher=

    2020

  14. [22]

    PRX quantum , volume=

    Theory of quantum system certification , author=. PRX quantum , volume=. 2021 , publisher=

    2021

  15. [23]

    Communications Physics , volume=

    Netsquid, a network simulator for quantum information using discrete events , author=. Communications Physics , volume=. 2021 , publisher=

    2021

  16. [24]

    Entanglement Distribution in Quantum Repeater with Purification and Optimized Buffer Time , year=

    Zang, Allen and Chen, Xinan and Kolar, Alexander and Chung, Joaquin and Suchara, Martin and Zhong, Tian and Kettimuthu, Rajkumar , booktitle=. Entanglement Distribution in Quantum Repeater with Purification and Optimized Buffer Time , year=

  17. [25]

    Quantum , volume=

    Entanglement buffering with two quantum memories , author=. Quantum , volume=. 2024 , publisher=

    2024

  18. [27]

    Physical Review Letters , volume=

    No-go theorems for universal entanglement purification , author=. Physical Review Letters , volume=. 2025 , publisher=

    2025

  19. [28]

    Physical Review A , volume=

    Quantum repeaters based on entanglement purification , author=. Physical Review A , volume=. 1999 , publisher=

    1999

  20. [29]

    Physical Review Letters , volume=

    Entanglement purification for quantum computation , author=. Physical Review Letters , volume=. 2003 , publisher=

    2003

  21. [30]

    SIAM Journal on Computing , volume=

    Privacy amplification by public discussion , author=. SIAM Journal on Computing , volume=. 1988 , publisher=

    1988

  22. [31]

    IEEE Transactions on Information Theory , volume=

    Generalized privacy amplification , author=. IEEE Transactions on Information Theory , volume=. 1995 , publisher=

    1995

  23. [32]

    Proceedings of Computational Complexity

    Randomized simultaneous messages: Solution of a problem of Yao in communication complexity , author=. Proceedings of Computational Complexity. Twelfth Annual IEEE Conference , pages=. 1997 , organization=

    1997

  24. [33]

    private coin flips in one round communication games , author=

    Public vs. private coin flips in one round communication games , author=. Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing , pages=

  25. [34]

    Common randomness in information theory and cryptography. I. Secret sharing , author=. IEEE Transactions on Information Theory , volume=. 1993 , publisher=

    1993

  26. [35]

    Physical Review Letters , volume=

    Communication cost of simulating Bell correlations , author=. Physical Review Letters , volume=. 2003 , publisher=

    2003

  27. [36]

    Physical Review Letters , volume=

    Distilling nonlocality , author=. Physical Review Letters , volume=. 2009 , publisher=

    2009

  28. [37]

    Physical Review Letters , volume=

    All entangled quantum states are nonlocal , author=. Physical Review Letters , volume=. 2012 , publisher=

    2012

  29. [38]

    Quantum , volume=

    The type-independent resource theory of local operations and shared randomness , author=. Quantum , volume=. 2020 , publisher=

    2020

  30. [39]

    Physical Review Letters , volume=

    Cost of exactly simulating quantum entanglement with classical communication , author=. Physical Review Letters , volume=. 1999 , publisher=

    1999

  31. [40]

    Physical Review Letters , volume=

    Local hidden variable models for entangled quantum states using finite shared randomness , author=. Physical Review Letters , volume=. 2015 , publisher=

    2015

  32. [41]

    Theoretical Computer Science , volume=

    Quantum cryptography: Public key distribution and coin tossing , author=. Theoretical Computer Science , volume=. 2014 , publisher=

    2014

  33. [42]

    Physical Review Letters , volume=

    Quantum cryptography based on Bell’s theorem , author=. Physical Review Letters , volume=. 1991 , publisher=

    1991

  34. [43]

    Quantum , volume=

    Quantum advantage for shared randomness generation , author=. Quantum , volume=. 2021 , publisher=

    2021

  35. [44]

    Bayesian

    Games with incomplete information played by “Bayesian” players, I--III Part I. The basic model , author=. Management Science , volume=. 1967 , publisher=

    1967

  36. [45]

    Physical Review A , volume=

    Standard forms of noisy quantum operations via depolarization , author=. Physical Review A , volume=. 2005 , publisher=

    2005

  37. [46]

    Science , volume=

    Symmetrized characterization of noisy quantum processes , author=. Science , volume=. 2007 , publisher=

    2007

  38. [47]

    Physical Review A , volume=

    Exact and approximate unitary 2-designs and their application to fidelity estimation , author=. Physical Review A , volume=. 2009 , publisher=

    2009

  39. [48]

    Physical Review A , volume=

    Optimal two-qubit gates in recurrence protocols of entanglement purification , author=. Physical Review A , volume=. 2022 , publisher=

    2022

  40. [49]

    Enumerating all bilocal

    Jansen, Sarah and Goodenough, Kenneth and de Bone, S. Enumerating all bilocal. Quantum , volume=. 2022 , publisher=

    2022

  41. [50]

    New Journal of Physics , volume=

    The dominant eigenvector of a noisy quantum state , author=. New Journal of Physics , volume=. 2021 , publisher=

    2021

  42. [52]

    PRX Quantum , volume =

    Faithfully Simulating Near-Term Quantum Repeaters , author =. PRX Quantum , volume =. 2024 , month =

    2024

  43. [53]

    Physical Review A , volume=

    Quantum data processing and error correction , author=. Physical Review A , volume=. 1996 , publisher=

    1996

  44. [54]

    Physical Review A , volume=

    Bound on distillable entanglement , author=. Physical Review A , volume=. 1999 , publisher=

    1999

  45. [55]

    IEEE Transactions on Information Theory , volume=

    A semidefinite program for distillable entanglement , author=. IEEE Transactions on Information Theory , volume=. 2001 , publisher=

    2001

  46. [56]

    Logarithmic negativity:

    Plenio, Martin B , journal=. Logarithmic negativity:. 2005 , publisher=

    2005

  47. [57]

    Physical Review Letters , volume=

    Entanglement of formation of an arbitrary state of two qubits , author=. Physical Review Letters , volume=. 1998 , publisher=

    1998

  48. [58]

    Physical Review Letters , volume=

    Entanglement of a pair of quantum bits , author=. Physical Review Letters , volume=. 1997 , publisher=

    1997

  49. [59]

    Physical Review Letters , volume=

    Quantifying entanglement , author=. Physical Review Letters , volume=. 1997 , publisher=

    1997

  50. [60]

    Physical Review A , volume=

    Entanglement measures and purification procedures , author=. Physical Review A , volume=. 1998 , publisher=

    1998

  51. [61]

    Reviews of Modern Physics , volume=

    The role of relative entropy in quantum information theory , author=. Reviews of Modern Physics , volume=. 2002 , publisher=

    2002

  52. [62]

    Everything you always wanted to know about

    Chitambar, Eric and Leung, Debbie and Man. Everything you always wanted to know about. Communications in Mathematical Physics , volume=. 2014 , publisher=

    2014

  53. [63]

    IEEE INFOCOM 2022-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS) , pages=

    Adaptive, continuous entanglement generation for quantum networks , author=. IEEE INFOCOM 2022-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS) , pages=. 2022 , organization=

    2022

  54. [64]

    2025 International Conference on Quantum Communications, Networking, and Computing (QCNC) , pages=

    Design and simulation of the adaptive continuous entanglement generation protocol , author=. 2025 International Conference on Quantum Communications, Networking, and Computing (QCNC) , pages=. 2025 , organization=

    2025

  55. [65]

    2024 IEEE International Conference on Quantum Computing and Engineering (QCE) , volume=

    Analytical performance estimations for quantum repeater network scenarios , author=. 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) , volume=. 2024 , organization=

    2024

  56. [66]

    Optics Express , volume=

    Purification of the residual entanglement , author=. Optics Express , volume=. 2020 , publisher=

    2020

  57. [67]

    Physical Review Letters , volume=

    Observation of Residual Entanglement in Entanglement Purification , author=. Physical Review Letters , volume=. 2025 , publisher=

    2025

  58. [69]

    Physical Review A , volume=

    Performance metrics for the continuous distribution of entanglement in multiuser quantum networks , author=. Physical Review A , volume=. 2023 , publisher=

    2023

  59. [70]

    2022 IEEE International Conference on Quantum Computing and Engineering (QCE) , pages=

    Pre-distribution of entanglements in quantum networks , author=. 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) , pages=. 2022 , organization=

    2022

  60. [71]

    Wu, Anbang and Ding, Yufei and Li, Ang , booktitle=

  61. [72]

    2025 62nd ACM/IEEE Design Automation Conference (DAC) , pages=

    Hardware-Software Co-design for Distributed Quantum Computing , author=. 2025 62nd ACM/IEEE Design Automation Conference (DAC) , pages=. 2025 , organization=

    2025

  62. [73]

    Reviews of Modern Physics , volume=

    Quantum resource theories , author=. Reviews of Modern Physics , volume=. 2019 , publisher=

    2019

  63. [74]

    Physical Review X , volume=

    Resource theory of quantum memories and their faithful verification with minimal assumptions , author=. Physical Review X , volume=. 2018 , publisher=

    2018

  64. [75]

    Quantum Science and Technology , volume=

    Quantum repeater architecture with hierarchically optimized memory buffer times , author=. Quantum Science and Technology , volume=. 2019 , publisher=

    2019

  65. [76]

    Communications Physics , volume=

    Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies , author=. Communications Physics , volume=. 2025 , publisher=

    2025

  66. [77]

    Physical Review Letters , volume=

    Constant overhead entanglement distillation via scrambling , author=. Physical Review Letters , volume=. 2026 , publisher=

    2026

  67. [78]

    Journal of Mathematical Physics , volume=

    Correlated entanglement distillation and the structure of the set of undistillable states , author=. Journal of Mathematical Physics , volume=. 2008 , publisher=

    2008

  68. [79]

    Physical Review Letters , volume=

    Renormalizing entanglement distillation , author=. Physical Review Letters , volume=. 2016 , publisher=

    2016

  69. [80]

    1997 , publisher=

    Stabilizer codes and quantum error correction , author=. 1997 , publisher=

    1997

  70. [81]

    2005 , school=

    Quantum communication in noisy environments , author=. 2005 , school=

    2005

  71. [82]

    PRX Quantum , volume=

    Practical introduction to benchmarking and characterization of quantum computers , author=. PRX Quantum , volume=. 2025 , publisher=

    2025

  72. [83]

    1979 , publisher=

    Inequalities: Theory of Majorization and Its Applications , author=. 1979 , publisher=

    1979

  73. [85]

    Distributed quantum information processing: a review of recent progress , journal =

    Kn. Distributed quantum information processing: a review of recent progress , journal =. 2026 , month =

    2026

  74. [86]

    IEEE Journal on Selected Areas in Communications , volume=

    Near-term n to k distillation protocols using graph codes , author=. IEEE Journal on Selected Areas in Communications , volume=. 2024 , publisher=

    2024

  75. [87]

    PRX Quantum , volume=

    Stabilizer entanglement distillation and efficient fault-tolerant encoders , author=. PRX Quantum , volume=. 2025 , publisher=

    2025

  76. [88]

    Physical Review Letters , volume=

    Constant-overhead fault-tolerant Bell-pair distillation using high-rate codes , author=. Physical Review Letters , volume=. 2025 , publisher=

    2025

  77. [89]

    ACM Transactions on Quantum Computing , volume=

    Efficient estimation of Pauli channels , author=. ACM Transactions on Quantum Computing , volume=. 2020 , publisher=

    2020

  78. [91]

    Nature Communications , volume=

    Detecting and tracking drift in quantum information processors , author=. Nature Communications , volume=. 2020 , publisher=

    2020

  79. [92]

    Proceedings of the forty-eighth annual ACM symposium on Theory of Computing , pages=

    Sample-optimal tomography of quantum states , author=. Proceedings of the forty-eighth annual ACM symposium on Theory of Computing , pages=

  80. [93]

    Nature Physics , volume=

    Predicting many properties of a quantum system from very few measurements , author=. Nature Physics , volume=. 2020 , publisher=

    2020

  81. [94]

    2023 , publisher=

    RFC 9340: Architectural principles for a quantum internet , author=. 2023 , publisher=

    2023

  82. [95]

    A link layer protocol for quantum networks , year =

    Dahlberg, Axel and Skrzypczyk, Matthew and Coopmans, Tim and Wubben, Leon and Rozp. A link layer protocol for quantum networks , year =. Proceedings of the ACM Special Interest Group on Data Communication , pages =

  83. [96]

    npj Quantum Information , volume=

    Experimental demonstration of entanglement delivery using a quantum network stack , author=. npj Quantum Information , volume=. 2022 , publisher=

    2022

  84. [97]

    Physical Review A , volume=

    Quantum key distribution with distinguishable decoy states , author=. Physical Review A , volume=. 2018 , publisher=

    2018

  85. [98]

    author author H. J. \ Kimble ,\ title title The quantum internet ,\ @noop journal journal Nature \ volume 453 ,\ pages 1023 ( year 2008 ) NoStop

    2008

  86. [99]

    Wehner , author D

    author author S. Wehner , author D. Elkouss ,\ and\ author R. Hanson ,\ title title Quantum internet: A vision for the road ahead ,\ @noop journal journal Science \ volume 362 ,\ pages eaam9288 ( year 2018 ) NoStop

    2018

  87. [100]

    Kn \"o rzer , author X

    author author J. Kn \"o rzer , author X. Liu , author B. Schiffer ,\ and\ author J. Tura Brugu \'e s ,\ title title Distributed quantum information processing: a review of recent progress ,\ @noop journal journal Reports on Progress in Physics \ volume 89 ,\ pages 074401 ( yea...

    2026

  88. [101]

    Muralidharan , author L

    author author S. Muralidharan , author L. Li , author J. Kim , author N. L \"u tkenhaus , author M. D. \ Lukin ,\ and\ author L. Jiang ,\ title title Optimal architectures for long distance quantum communication ,\ @noop journal journal Scientific Reports \ volume 6 ,\ pages 1...

    2016

  89. [102]

    Azuma , author S

    author author K. Azuma , author S. E. \ Economou , author D. Elkouss , author P. Hilaire , author L. Jiang , author H.-K. \ Lo ,\ and\ author I. Tzitrin ,\ title title Quantum repeaters: From quantum networks to the quantum internet ,\ @noop journal journal Reviews of Modern P...

    2023

  90. [103]

    author author C. H. \ Bennett , author G. Brassard , author S. Popescu , author B. Schumacher , author J. A. \ Smolin ,\ and\ author W. K. \ Wootters ,\ title title Purification of noisy entanglement and faithful teleportation via noisy channels ,\ @noop journal journal Physic...

    1996

  91. [104]

    Deutsch , author A

    author author D. Deutsch , author A. Ekert , author R. Jozsa , author C. Macchiavello , author S. Popescu ,\ and\ author A. Sanpera ,\ title title Quantum privacy amplification and the security of quantum cryptography over noisy channels ,\ @noop journal journal Physical Revie...

    1996

  92. [105]

    author author C. H. \ Bennett , author D. P. \ DiVincenzo , author J. A. \ Smolin ,\ and\ author W. K. \ Wootters ,\ title title Mixed-state entanglement and quantum error correction ,\ @noop journal journal Physical Review A \ volume 54 ,\ pages 3824 ( year 1996 b ) NoStop

    1996

  93. [106]

    D \"u r \ and\ author H

    author author W. D \"u r \ and\ author H. J. \ Briegel ,\ title title Entanglement purification and quantum error correction ,\ @noop journal journal Reports on Progress in Physics \ volume 70 ,\ pages 1381 ( year 2007 ) NoStop

    2007

  94. [107]

    Gottesman ,\ @noop title Stabilizer codes and quantum error correction \ ( publisher California Institute of Technology ,\ year 1997 ) NoStop

    author author D. Gottesman ,\ @noop title Stabilizer codes and quantum error correction \ ( publisher California Institute of Technology ,\ year 1997 ) NoStop

    1997

  95. [108]

    Zhou , author W

    author author L. Zhou , author W. Zhong ,\ and\ author Y.-B. \ Sheng ,\ title title Purification of the residual entanglement ,\ @noop journal journal Optics Express \ volume 28 ,\ pages 2291 ( year 2020 ) NoStop

    2020

  96. [109]

    Qin , author M.-M

    author author H. Qin , author M.-M. \ Du , author X.-Y. \ Li , author W. Zhong , author L. Zhou ,\ and\ author Y.-B. \ Sheng ,\ title title Efficient multipartite entanglement purification with non-identical states ,\ @noop journal journal arXiv preprint arXiv:2311.10250 \ ( y...

    2023 arXiv

  97. [110]

    Zang , author X

    author author A. Zang , author X. Chen , author E. Chitambar , author M. Suchara ,\ and\ author T. Zhong ,\ title title No-go theorems for universal entanglement purification ,\ @noop journal journal Physical Review Letters \ volume 134 ,\ pages 190803 ( year 2025 a ) NoStop

    2025

  98. [111]

    Zhou , author C.-X

    author author L. Zhou , author C.-X. \ Huang , author Y.-B. \ Sheng , author Y. Guo , author X.-M. \ Hu , author Y.-F. \ Huang , author C.-F. \ Li , author G.-C. \ Guo ,\ and\ author B.-H. \ Liu ,\ title title Observation of residual entanglement in entanglement purification ,...

    2025

  99. [112]

    Zang , author X.-A

    author author A. Zang , author X.-A. \ Chen , author E. Chitambar , author M. Suchara ,\ and\ author T. Zhong ,\ title title Entanglement purification in quantum networks: Guaranteed improvement and optimal time ,\ @noop journal journal arXiv preprint arXiv:2505.02286 \ ( year...

    2025 arXiv

  100. [113]

    Fayyaz , author P

    author author A. Fayyaz , author P. Krishnamurthy , author K. Seshadreesan , author A. Babay ,\ and\ author D. Tipper ,\ title title To purify or not to purify: Entanglement purification under input fidelity asymmetry in quantum networks ,\ @noop journal journal arXiv preprint...

    2026 arXiv

  101. [114]

    D \"u r , author H.-J

    author author W. D \"u r , author H.-J. \ Briegel , author J. I. \ Cirac ,\ and\ author P. Zoller ,\ title title Quantum repeaters based on entanglement purification ,\ @noop journal journal Physical Review A \ volume 59 ,\ pages 169 ( year 1999 ) NoStop

    1999

  102. [115]

    D \"u r \ and\ author H.-J

    author author W. D \"u r \ and\ author H.-J. \ Briegel ,\ title title Entanglement purification for quantum computation ,\ @noop journal journal Physical Review Letters \ volume 90 ,\ pages 067901 ( year 2003 ) NoStop

    2003

  103. [116]

    Chakraborty , author F

    author author K. Chakraborty , author F. Rozpedek , author A. Dahlberg ,\ and\ author S. Wehner ,\ title title Distributed routing in a quantum internet ,\ @noop journal journal arXiv preprint arXiv:1907.11630 \ ( year 2019 ) NoStop

    1907 arXiv

  104. [117]

    Kolar , author A

    author author A. Kolar , author A. Zang , author J. Chung , author M. Suchara ,\ and\ author R. Kettimuthu ,\ title title Adaptive, continuous entanglement generation for quantum networks ,\ in\ @noop booktitle IEEE INFOCOM 2022-IEEE Conference on Computer Communications Works...

    2022

  105. [118]

    Ghaderibaneh , author H

    author author M. Ghaderibaneh , author H. Gupta , author C. Ramakrishnan ,\ and\ author E. Luo ,\ title title Pre-distribution of entanglements in quantum networks ,\ in\ @noop booktitle 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) \ ( organiza...

    2022

  106. [119]

    Zang , author X

    author author A. Zang , author X. Chen , author A. Kolar , author J. Chung , author M. Suchara , author T. Zhong ,\ and\ author R. Kettimuthu ,\ title title Entanglement distribution in quantum repeater with purification and optimized buffer time ,\ in\ @noop booktitle IEEE IN...

    2023

  107. [120]

    author author \'A . G. \ I \ n esta \ and\ author S. Wehner ,\ title title Performance metrics for the continuous distribution of entanglement in multiuser quantum networks ,\ @noop journal journal Physical Review A \ volume 108 ,\ pages 052615 ( year 2023 ) NoStop

    2023

  108. [121]

    Davies , author \'A

    author author B. Davies , author \'A . G. \ I \ n esta ,\ and\ author S. Wehner ,\ title title Entanglement buffering with two quantum memories ,\ @noop journal journal Quantum \ volume 8 ,\ pages 1458 ( year 2024 ) NoStop

    2024

  109. [122]

    Zang , author J

    author author A. Zang , author J. Chung , author R. Kettimuthu , author M. Suchara ,\ and\ author T. Zhong ,\ title title Analytical performance estimations for quantum repeater network scenarios ,\ in\ @noop booktitle 2024 IEEE International Conference on Quantum Computing an...

    2024

  110. [123]

    Zhan , author J

    author author C. Zhan , author J. Chung , author A. Zang , author A. Kolar ,\ and\ author R. Kettimuthu ,\ title title Design and simulation of the adaptive continuous entanglement generation protocol ,\ in\ @noop booktitle 2025 International Conference on Quantum Communicatio...

    2025

  111. [124]

    Rozp e dek , author T

    author author F. Rozp e dek , author T. Schiet , author D. Elkouss , author A. C. \ Doherty , author S. Wehner , et al. ,\ title title Optimizing practical entanglement distillation ,\ @noop journal journal Physical Review A \ volume 97 ,\ pages 062333 ( year 2018 ) NoStop

    2018

  112. [125]

    Krastanov , author V

    author author S. Krastanov , author V. V. \ Albert ,\ and\ author L. Jiang ,\ title title Optimized entanglement purification ,\ @noop journal journal Quantum \ volume 3 ,\ pages 123 ( year 2019 ) NoStop

    2019

  113. [126]

    author author J. M. \ Martinis ,\ title title Qubit metrology for building a fault-tolerant quantum computer ,\ @noop journal journal npj Quantum Information \ volume 1 ,\ pages 1 ( year 2015 ) NoStop

    2015

  114. [127]

    Harper , author S

    author author R. Harper , author S. T. \ Flammia ,\ and\ author J. J. \ Wallman ,\ title title Efficient learning of quantum noise ,\ @noop journal journal Nature Physics \ volume 16 ,\ pages 1184 ( year 2020 ) NoStop

    2020

  115. [128]

    Eisert , author D

    author author J. Eisert , author D. Hangleiter , author N. Walk , author I. Roth , author D. Markham , author R. Parekh , author U. Chabaud ,\ and\ author E. Kashefi ,\ title title Quantum certification and benchmarking ,\ @noop journal journal Nature Reviews Physics \ volume ...

    2020

  116. [129]

    Kliesch \ and\ author I

    author author M. Kliesch \ and\ author I. Roth ,\ title title Theory of quantum system certification ,\ @noop journal journal PRX quantum \ volume 2 ,\ pages 010201 ( year 2021 ) NoStop

    2021

  117. [130]

    Hashim , author L

    author author A. Hashim , author L. B. \ Nguyen , author N. Goss , author B. Marinelli , author R. K. \ Naik , author T. Chistolini , author J. Hines , author J. P. \ Marceaux , author Y. Kim , author P. Gokhale , et al. ,\ title title Practical introduction to benchmarking an...

    2025

  118. [131]

    Wu , author Y

    author author A. Wu , author Y. Ding ,\ and\ author A. Li ,\ title title QuComm : Optimizing collective communication for distributed quantum computing ,\ in\ @noop booktitle Proceedings of the 56th Annual IEEE/ACM International Symposium on Microarchitecture \ ( year 2023 )\ ...

    2023

  119. [132]

    Liu , author A

    author author J. Liu , author A. Zang , author M. Suchara , author T. Zhong ,\ and\ author P. D. \ Hovland ,\ title title Hardware-software co-design for distributed quantum computing ,\ in\ @noop booktitle 2025 62nd ACM/IEEE Design Automation Conference (DAC) \ ( organization...

    2025

  120. [133]

    Jansen , author K

    author author S. Jansen , author K. Goodenough , author S. de Bone , author D. Gijswijt ,\ and\ author D. Elkouss ,\ title title Enumerating all bilocal Clifford distillation protocols through symmetry reduction ,\ @noop journal journal Quantum \ volume 6 ,\ pages 715 ( year 2...

    2022

  121. [134]

    @noop note Supplemental Material NoStop

  122. [135]

    \ Pan , author C

    author author J.-W. \ Pan , author C. Simon , author C . Brukner ,\ and\ author A. Zeilinger ,\ title title Entanglement purification for quantum communication ,\ @noop journal journal Nature \ volume 410 ,\ pages 1067 ( year 2001 ) NoStop

    2001

  123. [136]

    \ Pan , author S

    author author J.-W. \ Pan , author S. Gasparoni , author R. Ursin , author G. Weihs ,\ and\ author A. Zeilinger ,\ title title Experimental entanglement purification of arbitrary unknown states ,\ @noop journal journal Nature \ volume 423 ,\ pages 417 ( year 2003 ) NoStop

    2003

  124. [137]

    \ Hu , author C.-X

    author author X.-M. \ Hu , author C.-X. \ Huang , author Y.-B. \ Sheng , author L. Zhou , author B.-H. \ Liu , author Y. Guo , author C. Zhang , author W.-B. \ Xing , author Y.-F. \ Huang , author C.-F. \ Li , et al. ,\ title title Long-distance entanglement purification for q...

    2021

  125. [138]

    Ecker , author P

    author author S. Ecker , author P. Sohr , author L. Bulla , author M. Huber , author M. Bohmann ,\ and\ author R. Ursin ,\ title title Experimental single-copy entanglement distillation ,\ @noop journal journal Physical Review Letters \ volume 127 ,\ pages 040506 ( year 2021 ) NoStop

    2021

  126. [139]

    Reichle , author D

    author author R. Reichle , author D. Leibfried , author E. Knill , author J. Britton , author R. B. \ Blakestad , author J. D. \ Jost , author C. Langer , author R. Ozeri , author S. Seidelin ,\ and\ author D. J. \ Wineland ,\ title title Experimental purification of two-atom ...

    2006

  127. [140]

    Kalb , author A

    author author N. Kalb , author A. A. \ Reiserer , author P. C. \ Humphreys , author J. J. \ Bakermans , author S. J. \ Kamerling , author N. H. \ Nickerson , author S. C. \ Benjamin , author D. J. \ Twitchen , author M. Markham ,\ and\ author R. Hanson ,\ title title Entanglem...

    2017

  128. [141]

    Yan , author Y

    author author H. Yan , author Y. Zhong , author H.-S. \ Chang , author A. Bienfait , author M.-H. \ Chou , author C. R. \ Conner , author \'E . Dumur , author J. Grebel , author R. G. \ Povey ,\ and\ author A. N. \ Cleland ,\ title title Entanglement purification and protectio...

    2022

  129. [142]

    Preti , author T

    author author F. Preti , author T. Calarco , author J. M. \ Torres ,\ and\ author J. Z. \ Bern \'a d ,\ title title Optimal two-qubit gates in recurrence protocols of entanglement purification ,\ @noop journal journal Physical Review A \ volume 106 ,\ pages 022422 ( year 2022 ) NoStop

    2022

  130. [143]

    Goodenough , author S

    author author K. Goodenough , author S. De Bone , author V. Addala , author S. Krastanov , author S. Jansen , author D. Gijswijt ,\ and\ author D. Elkouss ,\ title title Near-term n to k distillation protocols using graph codes ,\ @noop journal journal IEEE Journal on Selected...

    2024

  131. [144]

    Shi , author A

    author author Y. Shi , author A. Patil ,\ and\ author S. Guha ,\ title title Stabilizer entanglement distillation and efficient fault-tolerant encoders ,\ @noop journal journal PRX Quantum \ volume 6 ,\ pages 010339 ( year 2025 ) NoStop

    2025

  132. [145]

    author author J. P. \ Bonilla Ataides , author H. Zhou , author Q. Xu , author G. Baranes , author B. Li , author M. D. \ Lukin ,\ and\ author L. Jiang ,\ title title Constant-overhead fault-tolerant bell-pair distillation using high-rate codes ,\ @noop journal journal Physica...

    2025

  133. [146]

    Li , author D

    author author B. Li , author D. Dilley , author A. Gonzales , author T. A. \ Hahn , author R. White , author R. Arnon , author H. Bernien , author Z. Saleem ,\ and\ author L. Jiang ,\ title title Efficient entanglement purification circuit design for dual-species atom arrays ,...

    2025

  134. [147]

    author author S. T. \ Flammia \ and\ author J. J. \ Wallman ,\ title title Efficient estimation of pauli channels ,\ @noop journal journal ACM Transactions on Quantum Computing \ volume 1 ,\ pages 1 ( year 2020 ) NoStop

    2020

  135. [148]

    author author A. W. \ Marshall \ and\ author I. Olkin ,\ @noop title Inequalities: Theory of Majorization and Its Applications \ ( publisher Academic Press ,\ address New York ,\ year 1979 ) NoStop

    1979

  136. [149]

    Forster , author S

    author author M. Forster , author S. Winkler ,\ and\ author S. Wolf ,\ title title Distilling nonlocality ,\ @noop journal journal Physical Review Letters \ volume 102 ,\ pages 120401 ( year 2009 ) NoStop

    2009

  137. [150]

    Buscemi ,\ title title All entangled quantum states are nonlocal ,\ @noop journal journal Physical Review Letters \ volume 108 ,\ pages 200401 ( year 2012 ) NoStop

    author author F. Buscemi ,\ title title All entangled quantum states are nonlocal ,\ @noop journal journal Physical Review Letters \ volume 108 ,\ pages 200401 ( year 2012 ) NoStop

    2012

  138. [151]

    Rosset , author F

    author author D. Rosset , author F. Buscemi ,\ and\ author Y.-C. \ Liang ,\ title title Resource theory of quantum memories and their faithful verification with minimal assumptions ,\ @noop journal journal Physical Review X \ volume 8 ,\ pages 021033 ( year 2018 ) NoStop

    2018

  139. [152]

    Chitambar \ and\ author G

    author author E. Chitambar \ and\ author G. Gour ,\ title title Quantum resource theories ,\ @noop journal journal Reviews of Modern Physics \ volume 91 ,\ pages 025001 ( year 2019 ) NoStop

    2019

  140. [153]

    Schmid , author D

    author author D. Schmid , author D. Rosset ,\ and\ author F. Buscemi ,\ title title The type-independent resource theory of local operations and shared randomness ,\ @noop journal journal Quantum \ volume 4 ,\ pages 262 ( year 2020 ) NoStop

    2020

  141. [154]

    author author F. G. \ Brand \ a o \ and\ author J. Eisert ,\ title title Correlated entanglement distillation and the structure of the set of undistillable states ,\ @noop journal journal Journal of Mathematical Physics \ volume 49 ( year 2008 ) NoStop

    2008

  142. [155]

    Waeldchen , author J

    author author S. Waeldchen , author J. Gertis , author E. T. \ Campbell ,\ and\ author J. Eisert ,\ title title Renormalizing entanglement distillation ,\ @noop journal journal Physical Review Letters \ volume 116 ,\ pages 020502 ( year 2016 ) NoStop

    2016

  143. [156]

    Gu , author L

    author author A. Gu , author L. Leone , author K. Goodenough ,\ and\ author S. Khatri ,\ title title Constant overhead entanglement distillation via scrambling ,\ @noop journal journal Physical Review Letters \ volume 136 ,\ pages 110805 ( year 2026 ) NoStop

    2026

  144. [157]

    Proctor , author M

    author author T. Proctor , author M. Revelle , author E. Nielsen , author K. Rudinger , author D. Lobser , author P. Maunz , author R. Blume-Kohout ,\ and\ author K. Young ,\ title title Detecting and tracking drift in quantum information processors ,\ @noop journal journal Na...

    2020

  145. [158]

    Haah , author A

    author author J. Haah , author A. W. \ Harrow , author Z. Ji , author X. Wu ,\ and\ author N. Yu ,\ title title Sample-optimal tomography of quantum states ,\ in\ @noop booktitle Proceedings of the forty-eighth annual ACM symposium on Theory of Computing \ ( year 2016 )\ pp.\ ...

    2016

  146. [159]

    \ Huang , author R

    author author H.-Y. \ Huang , author R. Kueng ,\ and\ author J. Preskill ,\ title title Predicting many properties of a quantum system from very few measurements ,\ @noop journal journal Nature Physics \ volume 16 ,\ pages 1050 ( year 2020 ) NoStop

    2020

  147. [160]

    Kozlowski , author S

    author author W. Kozlowski , author S. Wehner , author R. Van Meter , author B. Rijsman , author A. S. \ Cacciapuoti , author M. Caleffi ,\ and\ author S. Nagayama ,\ @noop title Rfc 9340: Architectural principles for a quantum internet ( year 2023 ) NoStop

    2023

  148. [161]

    Dahlberg , author M

    author author A. Dahlberg , author M. Skrzypczyk , author T. Coopmans , author L. Wubben , author F. Rozp e dek , author M. Pompili , author A. Stolk , author P. Pawe czak , author R. Knegjens , author J. de Oliveira Filho , author R. Hanson ,\ and\ author S. Wehner ,\ title t...

    2019

  149. [162]

    Pompili , author C

    author author M. Pompili , author C. Delle Donne , author I. te Raa , author B. van der Vecht , author M. Skrzypczyk , author G. Ferreira , author L. de Kluijver , author A. J. \ Stolk , author S. L. \ Hermans , author P. Pawe czak , et al. ,\ title title Experimental demonstr...

    2022

  150. [163]

    Huang , author S.-H

    author author A. Huang , author S.-H. \ Sun , author Z. Liu ,\ and\ author V. Makarov ,\ title title Quantum key distribution with distinguishable decoy states ,\ @noop journal journal Physical Review A \ volume 98 ,\ pages 012330 ( year 2018 ) NoStop

    2018

  151. [164]

    Chitambar , author D

    author author E. Chitambar , author D. Leung , author L. Man c inska , author M. Ozols ,\ and\ author A. Winter ,\ title title Everything you always wanted to know about LOCC (but were afraid to ask) ,\ @noop journal journal Communications in Mathematical Physics \ volume 328 ...

    2014

  152. [165]

    author author S. A. \ Hill \ and\ author W. K. \ Wootters ,\ title title Entanglement of a pair of quantum bits ,\ @noop journal journal Physical Review Letters \ volume 78 ,\ pages 5022 ( year 1997 ) NoStop

    1997

  153. [166]

    author author W. K. \ Wootters ,\ title title Entanglement of formation of an arbitrary state of two qubits ,\ @noop journal journal Physical Review Letters \ volume 80 ,\ pages 2245 ( year 1998 ) NoStop

    1998

  154. [167]

    author author M. B. \ Plenio ,\ title title Logarithmic negativity: A full entanglement monotone that is not convex ,\ @noop journal journal Physical Review Letters \ volume 95 ,\ pages 090503 ( year 2005 ) NoStop

    2005

  155. [168]

    author author E. M. \ Rains ,\ title title Bound on distillable entanglement ,\ @noop journal journal Physical Review A \ volume 60 ,\ pages 179 ( year 1999 ) NoStop

    1999

  156. [169]

    author author E. M. \ Rains ,\ title title A semidefinite program for distillable entanglement ,\ @noop journal journal IEEE Transactions on Information Theory \ volume 47 ,\ pages 2921 ( year 2001 ) NoStop

    2001

  157. [170]

    Vedral , author M

    author author V. Vedral , author M. B. \ Plenio , author M. A. \ Rippin ,\ and\ author P. L. \ Knight ,\ title title Quantifying entanglement ,\ @noop journal journal Physical Review Letters \ volume 78 ,\ pages 2275 ( year 1997 ) NoStop

    1997

  158. [171]

    Vedral \ and\ author M

    author author V. Vedral \ and\ author M. B. \ Plenio ,\ title title Entanglement measures and purification procedures ,\ @noop journal journal Physical Review A \ volume 57 ,\ pages 1619 ( year 1998 ) NoStop

    1998

  159. [172]

    Vedral ,\ title title The role of relative entropy in quantum information theory ,\ @noop journal journal Reviews of Modern Physics \ volume 74 ,\ pages 197 ( year 2002 ) NoStop

    author author V. Vedral ,\ title title The role of relative entropy in quantum information theory ,\ @noop journal journal Reviews of Modern Physics \ volume 74 ,\ pages 197 ( year 2002 ) NoStop

    2002

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