pith. machine review for the scientific record. sign in

arxiv: 2605.02840 · v1 · submitted 2026-05-04 · 🪐 quant-ph

Recognition: 3 theorem links

· Lean Theorem

Entanglement cost in non-local quantum computation

Alex May

Authors on Pith no claims yet

Pith reviewed 2026-05-08 18:04 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-local quantum computationentanglement costquantum cryptographyquantum complexityquantum gravitycommunication complexity
0
0 comments X

The pith

Entanglement cost in non-local quantum computation is closely tied to questions in cryptography, complexity, and gravity.

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

This paper reviews upper and lower bounds on the amount of shared entanglement needed to perform non-local quantum computation, a method that lets two distant quantum systems carry out a joint operation using only one round of communication plus pre-shared entanglement instead of direct interaction. A reader would care because these resource costs determine what is feasible in quantum cryptography protocols, computational tasks, communication problems, and models of quantum gravity. The review gathers known constructions that achieve certain operations with limited entanglement as well as proofs that some operations require large amounts. It also maps out how NLQC appears in multiple research areas and what the current bounds imply for each.

Core claim

The paper presents a comprehensive review of entanglement cost in NLQC, establishing that the quantity of shared entanglement required to implement joint unitaries on separated systems is a central object whose upper and lower bounds connect directly to open questions in quantum cryptography, computational complexity, communication complexity, quantum gravity, and related applications.

What carries the argument

Non-local quantum computation (NLQC), the process of realizing a joint quantum operation on two systems that never interact directly, using only pre-shared entanglement together with a single round of communication.

Load-bearing premise

The literature reviewed on upper and lower bounds is accurately and comprehensively summarized without major omissions or errors in interpretation.

What would settle it

A new explicit protocol that uses strictly less entanglement than the lowest upper bound summarized for a given task, or a new impossibility proof showing that a task requires more entanglement than the highest lower bound given, would contradict the review's account of the current state.

Figures

Figures reproduced from arXiv: 2605.02840 by Alex May.

Figure 1
Figure 1. Figure 1 view at source ↗
Figure 1
Figure 1. Figure 1 view at source ↗
Figure 1
Figure 1. Figure 1 view at source ↗
Figure 2
Figure 2. Figure 2 view at source ↗
Figure 2
Figure 2. Figure 2 view at source ↗
Figure 3
Figure 3. Figure 3 view at source ↗
Figure 3
Figure 3. Figure 3 view at source ↗
Figure 3
Figure 3. Figure 3 view at source ↗
Figure 3
Figure 3. Figure 3 view at source ↗
Figure 4
Figure 4. Figure 4 view at source ↗
Figure 4
Figure 4. Figure 4 view at source ↗
Figure 4
Figure 4. Figure 4 view at source ↗
Figure 5
Figure 5. Figure 5 view at source ↗
Figure 5
Figure 5. Figure 5 view at source ↗
Figure 5
Figure 5. Figure 5 view at source ↗
Figure 6
Figure 6. Figure 6 view at source ↗
Figure 6
Figure 6. Figure 6 view at source ↗
Figure 7
Figure 7. Figure 7 view at source ↗
Figure 7
Figure 7. Figure 7 view at source ↗
Figure 8
Figure 8. Figure 8 view at source ↗
Figure 8
Figure 8. Figure 8 view at source ↗
Figure 8
Figure 8. Figure 8 view at source ↗
Figure 9
Figure 9. Figure 9 view at source ↗
Figure 9
Figure 9. Figure 9 view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 11
Figure 11. Figure 11 view at source ↗
Figure 12
Figure 12. Figure 12 view at source ↗
read the original abstract

This is a book-length treatment of the subject of non-local quantum computation (NLQC). NLQC is a method for implementing quantum operations that interact two systems without directly bringing the systems together. Instead, a single round of communication and shared entanglement is used. NLQC has appeared in the context of quantum cryptography, computational complexity, communication complexity, quantum gravity, and other applications. The understanding of entanglement cost in NLQC is closely tied to questions in all of these areas. We review upper and lower bounds on entanglement cost, as well as some of the applications of NLQC and its connections to other subjects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript is a book-length review of non-local quantum computation (NLQC), a protocol for implementing quantum operations between two separated systems using only shared entanglement and one round of classical communication. It surveys known upper and lower bounds on the entanglement cost of such protocols and examines their connections to quantum cryptography, computational complexity, communication complexity, quantum gravity, and related applications. The central claim is that a thorough understanding of entanglement cost in NLQC is closely tied to open questions across these fields.

Significance. If the literature synthesis is accurate and comprehensive, the review provides a valuable consolidated reference for researchers working at the intersection of quantum information, cryptography, and gravity. By compiling bounds and highlighting interdisciplinary links without introducing new unverified derivations, it offers a foundation that could guide future work in these areas. The strength lies in the breadth of coverage and the explicit framing of NLQC entanglement cost as a unifying concept.

minor comments (2)
  1. Abstract: The abstract effectively outlines the scope but does not indicate the specific bounds or key results that will be emphasized, which would help readers assess relevance quickly.
  2. Given the book-length format, the manuscript would benefit from an explicit table of contents or section roadmap early in the introduction to improve navigability for readers consulting it as a reference.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary and assessment of the manuscript as a valuable consolidated reference on non-local quantum computation and its interdisciplinary connections. We note the recommendation for minor revision. Since the report contains no specific major comments or points requiring clarification, we have no point-by-point responses to provide. We will perform a final check for any minor issues such as typographical errors or updates to references to ensure the literature synthesis remains accurate and comprehensive.

Circularity Check

0 steps flagged

No circularity: synthesis review with no original derivations

full rationale

The manuscript is explicitly a book-length review that surveys and summarizes known upper and lower bounds on entanglement cost for NLQC protocols, along with their established links to cryptography, complexity, communication complexity, and quantum gravity. No new derivations, predictions, fitted parameters, or first-principles results are introduced; the text states that it reviews existing literature without presenting original equations or claims that could reduce to self-definitions or self-citations. All load-bearing content is therefore external to the paper and independently established in the cited prior work, rendering the derivation chain self-contained with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review paper, no new free parameters, axioms, or invented entities are introduced by the authors; the content synthesizes prior work.

pith-pipeline@v0.9.0 · 5379 in / 980 out tokens · 41262 ms · 2026-05-08T18:04:06.756077+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

71 extracted references · 10 canonical work pages · 1 internal anchor

  1. [1]

    Tagging systems, July 11 2006

    Adrian P Kent, William J Munro, Timothy P Spiller, and Raymond G Beausoleil. Tagging systems, July 11 2006. US Patent 7,075,438

    2006

  2. [2]

    Quantum tasks in holography.Journal of High Energy Physics, 2019(10):1–39, 2019

    Alex May. Quantum tasks in holography.Journal of High Energy Physics, 2019(10):1–39, 2019

    2019

  3. [3]

    Holographic scattering requires a connected entanglement wedge.Journal of High Energy Physics, 2020(8):1–34, 2020

    Alex May, Geoff Penington, and Jonathan Sorce. Holographic scattering requires a connected entanglement wedge.Journal of High Energy Physics, 2020(8):1–34, 2020

    2020

  4. [4]

    Relating non-local quantum computation to information theoretic cryptography.Quantum, 8:1387, 2024

    Rene Allerstorfer, Harry Buhrman, Alex May, Florian Speelman, and Philip Verduyn Lunel. Relating non-local quantum computation to information theoretic cryptography.Quantum, 8:1387, 2024

    2024

  5. [5]

    Magic and communication complexity.arXiv preprint arXiv:2510.07246, 2025

    Uma Girish, Alex May, Natalie Parham, and Henry Yuen. Magic and communication complexity.arXiv preprint arXiv:2510.07246, 2025

    work page arXiv 2025

  6. [6]

    Unclonable secret sharing

    Prabhanjan Ananth, Vipul Goyal, Jiahui Liu, and Qipeng Liu. Unclonable secret sharing. In International Conference on the Theory and Application of Cryptology and Information Security, pages 129–157. Springer, 2024

    2024

  7. [7]

    Security of quantum position-verification limits hamiltonian simulation via holography

    Harriet Apel, Toby Cubitt, Patrick Hayden, Tamara Kohler, and David Pérez-García. Security of quantum position-verification limits hamiltonian simulation via holography. Journal of High Energy Physics, 2024(8):1–40, 2024

    2024

  8. [8]

    Geometry of banach spaces: a new route towards position based cryptography.Communications in Mathematical Physics, 394(2):625–678, 2022

    Marius Junge, Aleksander M Kubicki, Carlos Palazuelos, and David Pérez-García. Geometry of banach spaces: a new route towards position based cryptography.Communications in Mathematical Physics, 394(2):625–678, 2022

    2022

  9. [9]

    Erweiterung des unbestimmtheitsprinzips für die relativistische quantentheorie.Zeitschrift für Physik, 69(1):56–69, 1931

    Lev Landau and Rudolf Peierls. Erweiterung des unbestimmtheitsprinzips für die relativistische quantentheorie.Zeitschrift für Physik, 69(1):56–69, 1931

    1931

  10. [10]

    Can we make sense out of the measurement process in relativistic quantum mechanics?Physical Review D, 24(2):359, 1981

    Yakir Aharonov and David Z Albert. Can we make sense out of the measurement process in relativistic quantum mechanics?Physical Review D, 24(2):359, 1981

    1981

  11. [11]

    Instantaneous measurement of nonlocal variables.Physical review letters, 90(1):010402, 2003

    Lev Vaidman. Instantaneous measurement of nonlocal variables.Physical review letters, 90(1):010402, 2003

    2003

  12. [12]

    Location-dependent communications using quantum entanglement

    Robert A Malaney. Location-dependent communications using quantum entanglement. Physical Review A—Atomic, Molecular, and Optical Physics, 81(4):042319, 2010

    2010

  13. [13]

    Quantum tagging: Authenticating location via quantum information and relativistic signaling constraints.Physical Review A—Atomic, Molecular, and Optical Physics, 84(1):012326, 2011

    Adrian Kent, William J Munro, and Timothy P Spiller. Quantum tagging: Authenticating location via quantum information and relativistic signaling constraints.Physical Review A—Atomic, Molecular, and Optical Physics, 84(1):012326, 2011

    2011

  14. [14]

    Position-based quantum cryptography: Impossibility and constructions.SIAM Journal on Computing, 43(1):150–178, 2014

    Harry Buhrman, Nishanth Chandran, Serge Fehr, Ran Gelles, Vipul Goyal, Rafail Ostrovsky, – 1 – and Christian Schaffner. Position-based quantum cryptography: Impossibility and constructions.SIAM Journal on Computing, 43(1):150–178, 2014

    2014

  15. [15]

    A monogamy-of-entanglement game with applications to device-independent quantum cryptography.New Journal of Physics, 15(10):103002, 2013

    Marco Tomamichel, Serge Fehr, Jędrzej Kaniewski, and Stephanie Wehner. A monogamy-of-entanglement game with applications to device-independent quantum cryptography.New Journal of Physics, 15(10):103002, 2013

    2013

  16. [16]

    Conditional disclosure of secrets with quantum resources.Quantum, 9:1885, 2025

    Vahid R Asadi, Kohdai Kuroiwa, Debbie Leung, Alex May, Sabrina Pasterski, and Chris Waddell. Conditional disclosure of secrets with quantum resources.Quantum, 9:1885, 2025

    2025

  17. [17]

    The garden-hose model

    Harry Buhrman, Serge Fehr, Christian Schaffner, and Florian Speelman. The garden-hose model. InProceedings of the 4th conference on Innovations in Theoretical Computer Science, pages 145–158, 2013

    2013

  18. [18]

    Code-routing: a new attack on position verification.Quantum, 7:1079, 2023

    Joy Cree and Alex May. Code-routing: a new attack on position verification.Quantum, 7:1079, 2023

    2023

  19. [19]

    New bounds for the garden-hose model.arXiv preprint arXiv:1412.4904, 2014

    Hartmut Klauck and Supartha Podder. New bounds for the garden-hose model.arXiv preprint arXiv:1412.4904, 2014

    work page arXiv 2014

  20. [20]

    Communication theory of secrecy systems.The Bell system technical journal, 28(4):656–715, 1949

    Claude E Shannon. Communication theory of secrecy systems.The Bell system technical journal, 28(4):656–715, 1949

    1949

  21. [21]

    Conditional disclosure of secrets via non-linear reconstruction

    Tianren Liu, Vinod Vaikuntanathan, and Hoeteck Wee. Conditional disclosure of secrets via non-linear reconstruction. InAnnual International Cryptology Conference, pages 758–790. Springer, 2017

    2017

  22. [22]

    Protecting data privacy in private information retrieval schemes

    Yael Gertner, Yuval Ishai, Eyal Kushilevitz, and Tal Malkin. Protecting data privacy in private information retrieval schemes. InProceedings of the thirtieth annual ACM symposium on Theory of computing, pages 151–160, 1998

    1998

  23. [23]

    Communication complexity of conditional disclosure of secrets and attribute-based encryption

    Romain Gay, Iordanis Kerenidis, and Hoeteck Wee. Communication complexity of conditional disclosure of secrets and attribute-based encryption. InAnnual Cryptology Conference, pages 485–502. Springer, 2015

    2015

  24. [24]

    On the power of amortization in secret sharing: d-uniform secret sharing and CDS with constant information rate.ACM Transactions on Computation Theory (TOCT), 12(4):1–21, 2020

    Benny Applebaum and Barak Arkis. On the power of amortization in secret sharing: d-uniform secret sharing and CDS with constant information rate.ACM Transactions on Computation Theory (TOCT), 12(4):1–21, 2020

    2020

  25. [25]

    Placing conditional disclosure of secrets in the communication complexity universe.Journal of Cryptology, 34:1–45, 2021

    Benny Applebaum and Prashant Nalini Vasudevan. Placing conditional disclosure of secrets in the communication complexity universe.Journal of Cryptology, 34:1–45, 2021

    2021

  26. [26]

    Conditional disclosure of secrets: Amplification, closure, amortization, lower-bounds, and separations

    Benny Applebaum, Barak Arkis, Pavel Raykov, and Prashant Nalini Vasudevan. Conditional disclosure of secrets: Amplification, closure, amortization, lower-bounds, and separations. In Annual International Cryptology Conference, pages 727–757. Springer, 2017

    2017

  27. [27]

    Private simultaneous messages protocols with applications

    Yuval Ishai and Eyal Kushilevitz. Private simultaneous messages protocols with applications. InProceedings of the Fifth Israeli Symposium on Theory of Computing and Systems, pages 174–183. IEEE, 1997

    1997

  28. [28]

    Comparing classical and quantum conditional disclosure of secrets, 2025

    Uma Girish, Alex May, Leo Orshansky, and Chris Waddell. Comparing classical and quantum conditional disclosure of secrets, 2025

    2025

  29. [29]

    Communication complexity of private simultaneous quantum messages protocols.arXiv preprint arXiv:2105.07120, 2021

    Akinori Kawachi and Harumichi Nishimura. Communication complexity of private simultaneous quantum messages protocols.arXiv preprint arXiv:2105.07120, 2021

    work page arXiv 2021

  30. [30]

    Asymptotic teleportation scheme as a universal programmable quantum processor.Physical review letters, 101(24):240501, 2008

    Satoshi Ishizaka and Tohya Hiroshima. Asymptotic teleportation scheme as a universal programmable quantum processor.Physical review letters, 101(24):240501, 2008. – 2 –

    2008

  31. [31]

    Simplified instantaneous non-local quantum computation with applications to position-based cryptography.New Journal of Physics, 13(9):093036, 2011

    Salman Beigi and Robert König. Simplified instantaneous non-local quantum computation with applications to position-based cryptography.New Journal of Physics, 13(9):093036, 2011

    2011

  32. [32]

    Programmable quantum gate arrays.Physical Review Letters, 79(2):321, 1997

    Michael A Nielsen and Isaac L Chuang. Programmable quantum gate arrays.Physical Review Letters, 79(2):321, 1997

    1997

  33. [33]

    Resource quantification for the no-programing theorem.Physical review letters, 122(8):080505, 2019

    Aleksander M Kubicki, Carlos Palazuelos, and David Pérez-García. Resource quantification for the no-programing theorem.Physical review letters, 122(8):080505, 2019

    2019

  34. [34]

    Instantaneous non-local computation of low t-depth quantum circuits

    Florian Speelman. Instantaneous non-local computation of low t-depth quantum circuits. arXiv preprint arXiv:1511.02839, 2015

    work page arXiv 2015

  35. [35]

    Popescu-rohrlich correlations imply efficient instantaneous nonlocal quantum computation.Physical Review A, 94(2):022318, 2016

    Anne Broadbent. Popescu-rohrlich correlations imply efficient instantaneous nonlocal quantum computation.Physical Review A, 94(2):022318, 2016

    2016

  36. [36]

    Exponential separation of quantum and classical communication complexity

    Ran Raz. Exponential separation of quantum and classical communication complexity. In Proceedings of the thirty-first annual ACM symposium on Theory of computing, pages 358–367, 1999

    1999

  37. [37]

    Quantum one-way communication can be exponentially stronger than classical communication

    Bo’az Klartag and Oded Regev. Quantum one-way communication can be exponentially stronger than classical communication. InProceedings of the 43rd ACM Symposium on Theory of Computing, San Jose, CA, USA, 6-8 June 2011, pages 31–40. ACM, 2011

    2011

  38. [38]

    Exponential separations for one-way quantum communication complexity, with applications to cryptography

    Dmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, Ran Raz, and Ronald de Wolf. Exponential separations for one-way quantum communication complexity, with applications to cryptography. InProceedings of the 39th Annual ACM Symposium on Theory of Computing, San Diego, California, USA, June 11-13, 2007, pages 516–525. ACM, 2007

    2007

  39. [39]

    Entangled simultaneity versus classical interactivity in communication complexity

    Dmitry Gavinsky. Entangled simultaneity versus classical interactivity in communication complexity. InProceedings of the forty-eighth annual ACM symposium on Theory of Computing, pages 877–884, 2016

    2016

  40. [40]

    Quantum versus randomized communication complexity, with efficient players.computational complexity, 31(2):17, 2022

    Uma Girish, Ran Raz, and Avishay Tal. Quantum versus randomized communication complexity, with efficient players.computational complexity, 31(2):17, 2022

    2022

  41. [41]

    One clean qubit suffices for quantum communication advantage.arXiv preprint arXiv:2310.02406, 2023

    Srinivasan Arunachalam, Uma Girish, and Noam Lifshitz. One clean qubit suffices for quantum communication advantage.arXiv preprint arXiv:2310.02406, 2023

    work page arXiv 2023

  42. [42]

    Quantum versus classical simultaneity in communication complexity, 2019

    Dmytro Gavinsky. Quantum versus classical simultaneity in communication complexity, 2019

    2019

  43. [43]

    Trade-offs between entanglement and communication

    Srinivasan Arunachalam and Uma Girish. Trade-offs between entanglement and communication. InProceedings of the 38th Computational Complexity Conference, CCC ’23, Dagstuhl, DEU, 2023. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik

    2023

  44. [44]

    Andreas Winter. Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints.Communications in Mathematical Physics, 347(1):291–313, 2016

    2016

  45. [45]

    Hill and W

    Scott Hill and William K Wootters. Entanglement of a pair of quantum bits.arXiv preprint quant-ph/9703041, 1997

    work page arXiv 1997

  46. [46]

    Entanglement of formation of an arbitrary state of two qubits.Physical Review Letters, 80(10):2245, 1998

    William K Wootters. Entanglement of formation of an arbitrary state of two qubits.Physical Review Letters, 80(10):2245, 1998

    1998

  47. [47]

    Mixed-state entanglement and quantum error correction.Physical Review A, 54(5):3824, 1996

    Charles H Bennett, David P DiVincenzo, John A Smolin, and William K Wootters. Mixed-state entanglement and quantum error correction.Physical Review A, 54(5):3824, 1996. – 3 –

    1996

  48. [48]

    Continuity bounds for entanglement.Physical review A, 61(6):064301, 2000

    Michael A Nielsen. Continuity bounds for entanglement.Physical review A, 61(6):064301, 2000

    2000

  49. [49]

    Randomized benchmarking with confidence.New Journal of Physics, 16(10):103032, 2014

    Joel J Wallman and Steven T Flammia. Randomized benchmarking with confidence.New Journal of Physics, 16(10):103032, 2014

    2014

  50. [50]

    Quantum coding.Physical review A, 51(4):2738, 1995

    Benjamin Schumacher. Quantum coding.Physical review A, 51(4):2738, 1995

    1995

  51. [51]

    Dina Abdelhadi and Joseph M Renes. On the second-order asymptotics of the partially smoothed conditional min-entropy & application to quantum compression.IEEE Journal on Selected Areas in Information Theory, 1(2):416–423, 2020

    2020

  52. [52]

    Lower bounds on non-local computation from controllable correlation

    Richard Cleve and Alex May. Lower bounds on non-local computation from controllable correlation.arXiv preprint arXiv:2602.00255, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  53. [53]

    Linear gate bounds against natural functions for position-verification.Quantum, 9:1604, 2025

    Vahid Asadi, Richard Cleve, Eric Culf, and Alex May. Linear gate bounds against natural functions for position-verification.Quantum, 9:1604, 2025

    2025

  54. [54]

    Communication complexity, 1996

    Eyal Kushilevitz and Noam Nisan. Communication complexity, 1996

    1996

  55. [55]

    Nondeterministic quantum query and communication complexities.SIAM Journal on Computing, 32(3):681–699, 2003

    Ronald De Wolf. Nondeterministic quantum query and communication complexities.SIAM Journal on Computing, 32(3):681–699, 2003

    2003

  56. [56]

    Rank lower bounds on non-local quantum computation.arXiv preprint arXiv:2402.18647, 2024

    Vahid R Asadi, Eric Culf, and Alex May. Rank lower bounds on non-local quantum computation.arXiv preprint arXiv:2402.18647, 2024

    work page arXiv 2024

  57. [57]

    A single-qubit position verification protocol that is secure against multi-qubit attacks.Nature Physics, 18(6):623–626, 2022

    Andreas Bluhm, Matthias Christandl, and Florian Speelman. A single-qubit position verification protocol that is secure against multi-qubit attacks.Nature Physics, 18(6):623–626, 2022

    2022

  58. [58]

    The connected wedge theorem and its consequences.Journal of High Energy Physics, 2022(11):1–65, 2022

    Alex May, Jonathan Sorce, and Beni Yoshida. The connected wedge theorem and its consequences.Journal of High Energy Physics, 2022(11):1–65, 2022

    2022

  59. [59]

    Quantum detection and estimation theory.Journal of statistical physics, 1(2):231–252, 1969

    Carl W Helstrom. Quantum detection and estimation theory.Journal of statistical physics, 1(2):231–252, 1969

    1969

  60. [60]

    Cambridge university press, 2013

    Mark M Wilde.Quantum information theory. Cambridge university press, 2013

    2013

  61. [61]

    On quantum rényi entropies: A new generalization and some properties.Journal of Mathematical Physics, 54(12), 2013

    Martin Müller-Lennert, Frédéric Dupuis, Oleg Szehr, Serge Fehr, and Marco Tomamichel. On quantum rényi entropies: A new generalization and some properties.Journal of Mathematical Physics, 54(12), 2013

    2013

  62. [62]

    Strong converse for the classical capacity of entanglement-breaking and hadamard channels via a sandwiched rényi relative entropy

    Mark M Wilde, Andreas Winter, and Dong Yang. Strong converse for the classical capacity of entanglement-breaking and hadamard channels via a sandwiched rényi relative entropy. Communications in Mathematical Physics, 331(2):593–622, 2014

    2014

  63. [63]

    Robustness of entanglement.Physical Review A, 59(1):141, 1999

    Guifré Vidal and Rolf Tarrach. Robustness of entanglement.Physical Review A, 59(1):141, 1999

    1999

  64. [64]

    Dimensional Reduction in Quantum Gravity

    Gerardt Hooft. Dimensional reduction in quantum gravity.arXiv preprint gr-qc/9310026, 1993

    work page Pith review arXiv 1993

  65. [65]

    The world as a hologram.Journal of Mathematical Physics, 36(11):6377–6396, 1995

    Leonard Susskind. The world as a hologram.Journal of Mathematical Physics, 36(11):6377–6396, 1995

    1995

  66. [66]

    A covariant entropy conjecture.Journal of High Energy Physics, 1999(07):004–004, 1999

    Raphael Bousso. A covariant entropy conjecture.Journal of High Energy Physics, 1999(07):004–004, 1999

    1999

  67. [67]

    Ultimate physical limits to computation.Nature, 406(6799):1047–1054, 2000

    Seth Lloyd. Ultimate physical limits to computation.Nature, 406(6799):1047–1054, 2000. – 4 –

    2000

  68. [68]

    Complexity and entanglement in non-local computation and holography

    Alex May. Complexity and entanglement in non-local computation and holography. Quantum, 6:864, 2022

    2022

  69. [69]

    A complexity theory for non-local quantum computation.arXiv preprint arXiv:2505.23893, 2025

    Andreas Bluhm, Simon Höfer, Alex May, Mikka Stasiuk, Philip Verduyn Lunel, and Henry Yuen. A complexity theory for non-local quantum computation.arXiv preprint arXiv:2505.23893, 2025

    work page arXiv 2025

  70. [70]

    Non-local quantum computation reductions beyond cliffords.to appear, 2026

    Andreas Bluhm, Simon Hofer, Alex May, Florian Speelman, and Philip Verduyn Lunel. Non-local quantum computation reductions beyond cliffords.to appear, 2026

    2026

  71. [71]

    Device-independent quantum position verification

    Gautam A Kavuri, Abigail Gookin, Yanbao Zhang, Joshua C Bienfang, Honghao Fu, Yusuf Alnawakhtha, Soumyadip Patra, Dileep V Reddy, Michael D Mazurek, Carlos Abellán, et al. Device-independent quantum position verification. InQuantum 2.0, pages QM3B–3. Optica Publishing Group, 2025. – 5 –

    2025