pith. sign in

arxiv: 2510.01951 · v2 · pith:CWTOUL5Mnew · submitted 2025-10-02 · 🪐 quant-ph

Maximum heralding probabilities of nonclassical-state generation from a two-mode Gaussian state via photon-counting measurements

Jarom\'ir Fiur\'a\v{s}ek This is my paper

Pith reviewed 2026-05-21 21:42 UTC · model grok-4.3

classification 🪐 quant-ph
keywords heralding probabilitynonclassical statesGaussian statesphoton countingtwo-mode entanglementpolynomial scalingstellar ranksqueezed light
0
0 comments X

The pith

The maximum heralding probability for nonclassical states from two-mode Gaussian inputs via photon counting admits an exact analytical formula.

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

The paper establishes that the highest success probability for heralding a nonclassical state by counting n photons on one mode of a two-mode entangled Gaussian state can be obtained through an exact analytical expression. A sympathetic reader cares because this probability fixes the generation rate, so knowing its scaling with n directly informs how feasible the scheme is for producing useful quantum states. The work shows that the number of experimental trials required grows only polynomially with n. This scaling implies that states of high complexity remain reachable in principle whenever the input squeezing can be made sufficiently strong.

Core claim

The maximum heralding probability for the two-mode setting can be calculated analytically, and its dependence on the number of detected photons n is investigated. The number of required experimental trials scales only polynomially with n. Generation of highly complex optical quantum states with high stellar rank is thus in principle possible in this setting, given access to sufficiently strong squeezing.

What carries the argument

Analytical maximization of the heralding probability over the parameters of the two-mode Gaussian input state, yielding a closed-form expression in n.

Load-bearing premise

The input is an ideal two-mode entangled Gaussian state whose squeezing parameter can be made arbitrarily large with no loss.

What would settle it

Numerical maximization of the heralding probability over all possible two-mode Gaussian states for a fixed small n should exactly reproduce the analytical maximum value derived in the paper.

Figures

Figures reproduced from arXiv: 2510.01951 by Jarom\'ir Fiur\'a\v{s}ek.

Figure 1
Figure 1. Figure 1: FIG. 1. Conditional state preparation via Gaussian boson [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dependence of the heralding probability [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The maximum heralding probability [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Highly nonclassical states of light - such as the approximate Gottesman-Kitaev-Preskill states, states exhibiting cubic nonlinear squeezing, or cat-like states - can be generated from experimentally accessible Gaussian states via photon counting measurements on selected modes, conditioned on specific outcomes of these heralding events. A simplest yet important example of this approach involves performing photon number measurements on one mode of a two-mode entangled Gaussian state. The heralding probability of this scheme is a key figure of merit, as it determines the generation rate of the target nonclassical state. In this work we show that the maximum heralding probability for the two-mode setting can be calculated analytically, and we investigate its dependence on the number of detected photons n. Our results show that the number of required experimental trials scales only polynomially with n. Generation of highly complex optical quantum states with high stellar rank is thus in principle possible in this setting, given access to sufficiently strong squeezing.

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

2 major / 3 minor

Summary. The manuscript derives an analytical expression for the maximum heralding probability achievable when generating nonclassical states (such as approximate GKP or cat states) from an ideal two-mode entangled Gaussian state by performing photon-number-resolving measurements on one mode and conditioning on the detection of exactly n photons. It shows that this maximum probability implies that the number of experimental trials required scales only polynomially with n, provided the squeezing parameter can be made sufficiently large in the lossless case.

Significance. If the central analytical result holds, the work establishes a concrete efficiency benchmark for a minimal heralding protocol, demonstrating that high stellar-rank nonclassical states can be targeted with only polynomial overhead in the ideal setting. This is a useful reference point for assessing the resource requirements of Gaussian-to-non-Gaussian conversion schemes and correctly qualifies the result by its dependence on strong squeezing.

major comments (2)
  1. [§3] §3, around Eq. (12)–(15): the optimization over the two-mode squeezing parameter r that yields the maximum heralding probability P_max(n) is presented, but the final closed-form expression for P_max(n) itself is not written out explicitly. Without this formula it is difficult to verify the precise polynomial degree of the scaling of 1/P_max(n) with n or to reproduce the result independently.
  2. [§4] §4, paragraph following Eq. (20): the statement that the optimal mean photon number remains O(1) independent of n is central to the polynomial-scaling claim, yet no explicit bound or asymptotic analysis is supplied showing how P_max(n) behaves for large n; a short derivation or plot of the scaling exponent would make the claim load-bearing rather than asserted.
minor comments (3)
  1. [Abstract] The abstract and introduction use the phrase 'sufficiently strong squeezing' without a quantitative estimate of the required r(n); adding a brief remark or inset in Figure 2 would help readers assess experimental accessibility.
  2. [§2.1] Notation for the two-mode covariance matrix in §2.1 is introduced without an explicit reference to the standard symplectic form; a single sentence recalling the parametrization would improve readability for non-specialists.
  3. [Figure 3] Figure 3 caption does not state the range of squeezing values over which the numerical check was performed; this makes it harder to judge how close the plotted points are to the claimed analytical maximum.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and the recommendation for minor revision. The comments help strengthen the clarity and verifiability of our analytical results on the maximum heralding probability. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: §3, around Eq. (12)–(15): the optimization over the two-mode squeezing parameter r that yields the maximum heralding probability P_max(n) is presented, but the final closed-form expression for P_max(n) itself is not written out explicitly. Without this formula it is difficult to verify the precise polynomial degree of the scaling of 1/P_max(n) with n or to reproduce the result independently.

    Authors: We agree that an explicit closed-form expression for P_max(n) improves clarity and reproducibility. In the revised manuscript we have added the closed-form expression obtained from the optimization over r immediately after the discussion of Eqs. (12)–(15). This expression directly confirms the polynomial scaling of 1/P_max(n) with n and enables independent verification of the result. revision: yes

  2. Referee: §4, paragraph following Eq. (20): the statement that the optimal mean photon number remains O(1) independent of n is central to the polynomial-scaling claim, yet no explicit bound or asymptotic analysis is supplied showing how P_max(n) behaves for large n; a short derivation or plot of the scaling exponent would make the claim load-bearing rather than asserted.

    Authors: We appreciate the suggestion to make the scaling claim more explicit. In the revised Section 4 we have added a short asymptotic analysis following Eq. (20) that derives an explicit bound showing the optimal mean photon number remains O(1) independent of n. We also provide the leading-order scaling of P_max(n) for large n, confirming polynomial behavior, and include a brief illustration of the scaling exponent. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives an analytical expression for the maximum heralding probability by optimizing the parameters (primarily squeezing strength) of an ideal two-mode entangled Gaussian state for photon-number heralding on one mode. The resulting polynomial scaling of required trials with n follows directly from the optimization result that the optimal mean photon number remains O(1). This is a self-contained mathematical calculation under the stated assumptions of lossless ideal Gaussian states with arbitrarily large but finite squeezing; no steps reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations. The central claim is explicitly conditioned on access to sufficiently strong squeezing and does not rely on external benchmarks or prior author-specific uniqueness theorems.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of quantum optics about Gaussian states and ideal photon-number-resolving detectors; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Two-mode entangled Gaussian states with tunable squeezing can be prepared and subjected to photon-number measurements on one mode.
    This is the experimental setup presupposed by the heralding scheme.

pith-pipeline@v0.9.0 · 5699 in / 1289 out tokens · 50818 ms · 2026-05-21T21:42:32.715345+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.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Heralding probability optimization for nonclassical light generated by photon counting measurements on multimode Gaussian states

    quant-ph 2026-04 unverdicted novelty 7.0

    Maximization of heralding probability in photon-counting schemes on multimode Gaussian states reduces to solving a system of polynomial equations.

Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · cited by 1 Pith paper · 2 internal anchors

  1. [1]

    Maximum heralding probabilities of nonclassical-state generation from a two-mode Gaussian state via photon-counting measurements

    listopadu 12, 77900 Olomouc, Czech Republic Highly non-classical states of light — such as the approximate Gottesman-Kitaev-Preskill states or cat-like states — can be generated from experimentally accessible Gaussian states via photon counting measurements on selected modes, conditioned on specific outcomes of these heralding events. A simplest yet impor...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    A. P. Lund, A. Laing, S. Rahimi-Keshari, T. Rudolph, J. L. O’Brien, and T. C. Ralph, Boson Sampling from a Gaussian State, Phys. Rev. Lett.113, 100502 (2014)

    work page 2014

  3. [3]

    C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Gaussian Boson Sampling, Phys. Rev. Lett.119, 170501 (2017)

    work page 2017

  4. [4]

    Paesani, Y

    S. Paesani, Y. Ding, R. Santagati, L. Chakhmakhchyan, Ca. Vigliar, K. Rottwitt, L. K. Oxenløwe, J. Wang, M. G. Thompson, and A. Laing, Generation and sampling of quantum states of light in a silicon chip, Nature Physics 15, 925 (2019)

    work page 2019

  5. [5]

    Zhong, H

    H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan , G. Yang, L. You, Z. Wang, L. Li , N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Quantum computational advantage using photons, Science370, 1460 (2020)

    work page 2020

  6. [6]

    Zhong, Y.-H

    H.-S. Zhong, Y.-H. Deng, J. Qin, H. Wang, M.-C. Chen, L.-C. Peng, Y.-H. Luo, D. Wu, S.-Q. Gong, H. Su, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, 7 L. Gan, G. Yang, L. You, Z, Wang, L. Li, N.-L. Liu, J. J. Renema, C.-Y. Lu, and J.-W. Pan, Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light, Phys. Rev. Lett.127, 1...

    work page 2021

  7. [7]

    Thekkadath, S

    G.S. Thekkadath, S. Sempere-Llagostera, B.A. Bell, R.B. Patel, M.S. Kim, and I.A. Walmsley, Experimental Demonstration of Gaussian Boson Sampling with Dis- placement, PRX Quantum3, 020336 (2022)

    work page 2022

  8. [8]

    C. Oh, M. Liu, Y. Alexeev, B. Fefferman and L. Jiang, Classical algorithm for simulating experimental Gaussian boson sampling, Nature Physics20, 1461 (2024)

    work page 2024

  9. [9]

    D. Su, C. R. Myers, and K. K. Sabapathy, Conversion of Gaussian states to non-Gaussian states using photon- number-resolving detectors, Phys. Rev. A100, 052301 (2019)

    work page 2019

  10. [10]

    Takase, K

    K. Takase, K. Fukui, A. Kawasaki, W. Asavanant, M. Endo, J.-i. Yoshikawa, P. van Loock, and A. Furusawa, Gottesman-Kitaev-Preskill qubit synthesizer for propa- gating light, npj Quantum Inf.9, 98 (2023)

    work page 2023

  11. [11]

    M. V. Larsen, J. E. Bourassa, S. Kocsis, J. F. Tasker, R. S. Chadwick, C. Gonz´ alez-Arciniegas, J. Hastrup, C. E. Lopetegui-Gonz´ alez, F. M. Miatto, A. Motamedi, R. Noro, G. Roeland, R. Baby, H. Chen, P. Contu, I. Di Luch, C. Drago, M. Giesbrecht, T. Grainge, I. Krasnokutska, M. Menotti, B. Morrison, C. Puviraj, K. Rezaei Shad, B. Hussain, J. McMahon, J...

    work page 2025

  12. [12]

    Beyond Stellar Rank: Control Parameters for Scalable Optical Non-Gaussian State Generation

    F. Hanamura, K. Takase, H. Nagayoshi, R. Ide, W. Asavanant, K. Fukui, P. Marek, R. Filip, and A. Furusawa, Beyond Stellar Rank: Control Parameters for Scalable Optical Non-Gaussian State Generation, arXiv:2509.06255

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [13]

    A. I. Lvovsky, P. Grangier, A. Ourjoumtsev, V. Pa- rigi, M. Sasaki, and R. Tualle-Brouri, Production and applications of non-Gaussian quantum states of light, arXiv:2006.16985, (2020)

    work page arXiv 2006

  14. [14]

    Biagi, S

    N. Biagi, S. Francesconi, A. Zavatta, and M. Bellini, Photon-by-photon quantum light state engineering, Prog. Quant. Electron.84, 100414 (2022)

    work page 2022

  15. [15]

    Zavatta, S

    A. Zavatta, S. Viciani, and M. Bellini, Quantum-to- Classical Transition with Single-Photon-Added Coherent States of Light, Science306, 660 (2004)

    work page 2004

  16. [16]

    Barbieri, N

    M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferrey- rol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, Non-gaussianity of quantum states: An experimental test on single-photon-added coherent states, Phys. Rev. A82, 063833 (2010)

    work page 2010

  17. [17]

    Kumar, E

    R. Kumar, E. Barrios, C. Kupchak, and A. I. Lvovsky, Experimental Characterization of Bosonic Creation and Annihilation Operators, Phys. Rev. Lett.110, 130403 (2013)

    work page 2013

  18. [18]

    Fadrn´ y, M

    J. Fadrn´ y, M. Neset, M. Bielak, M. Jeˇ zek, J. B´ ılek, and J. Fiur´ aˇ sek, Experimental preparation of multiphoton- added coherent states of light, npj Quantum Inf.10, 89 (2024)

    work page 2024

  19. [19]

    Chen, H.-Y

    Y.-R. Chen, H.-Y. Hsieh, J. Ning, H.-C. Wu, H. L. Chen, Z.-H. Shi, P. Yang, O. Steuernagel, C.-M. Wu, and R.-K. Lee, Generation of heralded optical cat states by photon addition, Phys. Rev. A110, 023703 (2024)

    work page 2024

  20. [20]

    Ourjoumtsev, R

    A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, Generating optical Schr¨ odinger kittens for quantum information processing, Science312, 83 (2006)

    work page 2006

  21. [21]

    J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Molmer, and E. S. Polzik, Generation of a superposition of odd photon number states for quantum information networks, Phys. Rev. Lett.97, 083604 (2006)

    work page 2006

  22. [22]

    Wakui, H

    K. Wakui, H. Takahashi, A. Furusawa, and M. Sasaki, Photon subtracted squeezed states generated with peri- odically poled KTiOPO 4, Opt. Express15, 3568 (2007)

    work page 2007

  23. [23]

    J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Optical continuous-variable qubit, Phys. Rev. Lett.105, 053602 (2010)

    work page 2010

  24. [24]

    Huang, H

    K. Huang, H. Le Jeannic, J. Ruaudel, V. B. Verma, M. D. Shaw, F. Marsili, S. W. Nam, E Wu, H. Zeng, Y.-C. Jeong, R. Filip, O. Morin, and J. Laurat, Optical syn- thesis of large-amplitude squeezed coherent-state super- positions with minimal resources, Phys. Rev. Lett.115, 023602 (2015)

    work page 2015

  25. [25]

    M. Endo, T. Nomura, T. Sonoyama, K. Takahashi, S. Takasu, D. Fukuda, T. Kashiwazaki, A. Inoue, T. Umeki, R. Nehra, P. Marek, R. Filip, K. Takase, W. Asavanant, and A. Furusawa, High-Rate Four Photon Subtraction from Squeezed Vacuum: Preparing Cat State for Optical Quantum Computation, arXiv:2502.08952 (2025)

    work page arXiv 2025

  26. [26]

    A. E. Lita, A. J. Miller, and S. W. Nam, Counting near- infrared single-photons with 95% efficiency, Opt. Express 16, 3032 (2008)

    work page 2008

  27. [27]

    Eaton, A

    M. Eaton, A. Hossameldin, R. J. Birrittella, P. M. Alsing, C. C. Gerry, H. Dong, C. Cuevas, and O. Pfister, Resolu- tion of 100 photons and quantum generation of unbiased random numbers, Nat. Photon.17, 106 (2023)

    work page 2023

  28. [28]

    J. W. N. Los, M. Sidorova, B. Lopez-Rodriguez, P. Qualm, J. Chang, S. Steinhauer, V. Zwiller, and I. E. Zadeh, High-performance photon number resolving de- tectors for 850–950 nm wavelength range, APL Photonics 9, 066101 (2024)

    work page 2024

  29. [29]

    Aghaee Rad, T

    H. Aghaee Rad, T. Ainsworth, R. N. Alexander, B. Al- tieri, M. F. Askarani, R. Baby, L. Banchi, B. Q. Bara- giola, J. E. Bourassa, R. S. Chadwick, I. Charania, H. Chen, M. J. Collins, P. Contu, N. D’Arcy, G. Dauphi- nais, R. De Prins, D. Deschenes, I. Di Luch, S. Duque, P. Edke, S. E. Fayer, S. Ferracin, H. Ferretti, J. Gefaell, S. Glancy, C. Gonz´ alez-A...

    work page 2025

  30. [30]

    Takase, J.-I

    K. Takase, J.-I. Yoshikawa, W. Asavanant, M. Endo, and A. Furusawa, Generation of optical Schr¨ odinger cat states by generalized photon subtraction, Phys. Rev. A103, 013710 (2021). 8

    work page 2021

  31. [31]

    Tomoda, A

    H. Tomoda, A. Machinaga, K. Takase, J. Harada, T. Kashiwazaki, T.i Umeki, S. Miki, F. China, M. Yabuno, H. Terai, D. Okuno, and S. Takeda, Boosting the genera- tion rate of squeezed single-photon states by generalized photon subtraction, Phys. Rev. A110, 033717 (2024)

    work page 2024

  32. [32]

    Takase, F

    K. Takase, F. Hanamura, H. Nagayoshi, J. E. Bourassa, R. N. Alexander, A. Kawasaki, W. Asavanant, M. Endo, and A. Furusawa, Generation of flying logical qubits us- ing generalized photon subtraction with adaptive Gaus- sian operations, Phys. Rev. A110, 012436 (2024)

    work page 2024

  33. [33]

    Chabaud, D

    U. Chabaud, D. Markham, and F. Grosshans, Stellar Representation of Non-Gaussian Quantum States, Phys. Rev. Lett.124, 063605 (2020)

    work page 2020

  34. [34]

    Chabaud, G

    [U. Chabaud, G. Roeland, M. Walschaers, F. C. Grosshans, V. Parigi, D. Markham, and N. Treps, Cer- tification of Non-Gaussian States with Operational Mea- surements, PRX Quantum.2, 020333 (2021)

    work page 2021

  35. [35]

    Lachman, I

    L. Lachman, I. Straka, J. Hlouˇ sek, M. Jeˇ zek, and R. Filip, Faithful Hierarchy of Genuine n-Photon Quantum Non- Gaussian Light, Phys. Rev. Lett.123, 043601 (2019)

    work page 2019

  36. [36]

    A Vourdas, Analytic representations in quantum me- chanics, J. Phys. A: Math. Gen.39, R65 (2006)

    work page 2006

  37. [37]

    Motamedi, Y

    A. Motamedi, Y. Yao, K. Nielsen, U. Chabaud, J. E. Bourassa, R. N. Alexander, and F. Miatto, The stellar decomposition of Gaussian quantum states, arXiv:2504.10455

    work page arXiv

  38. [38]

    S. L. Braunstein, Squeezing as an irreducible resource, Phys. Rev. A71, 055801 (2005)

    work page 2005

  39. [39]

    (1915), Sur les matrices hypohermitiennes et sur les matrices unitaires, Ann

    Autonne, L. (1915), Sur les matrices hypohermitiennes et sur les matrices unitaires, Ann. Univ. Lyon38, 1 (1915)

    work page 1915

  40. [40]

    Takagi, On an algebraic problem related to an ana- lytic theorem of Carath´ eodory and Fej´ er and on an allied theorem of Landau, Jpn

    T. Takagi, On an algebraic problem related to an ana- lytic theorem of Carath´ eodory and Fej´ er and on an allied theorem of Landau, Jpn. J. Math.1, 83 (1925)

    work page 1925

  41. [41]

    S. B. Korolev, E. N. Bashmakova, and T. Yu Golubeva, Laser Physics Letters21, 095204 (2024)

    work page 2024

  42. [42]

    S. B. Korolev and T. Yu. Golubeva, Bosonic error correc- tion codes based on states generated via particle number resolving measurements, arXiv:2509.16993

    work page arXiv

  43. [43]

    S. B. Korolev, E. N. Bashmakova, A. K. Tagantsev, and T. Y. Golubeva, Generation of squeezed Fock states by measurement, Phys. Rev. A109, 052428 (2024)

    work page 2024

  44. [44]

    Szeg˝ o, Orthogonal Polynomials, Amer

    G. Szeg˝ o, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc., Providence, RI, fourth edition, 1975

    work page 1975

  45. [45]

    ´Alvarez-Nodarse and J

    R. ´Alvarez-Nodarse and J. J. Moreno-Balc´ azar, Asymp- totic properties of generalized Laguerre orthogonal poly- nomials, Indagationes Mathematicae15, 151 (2004)

    work page 2004

  46. [46]

    G. S. Agarwal and K. Tara, Nonclassical properties of states generated by the excitations on a coherent state, Phys. Rev. A43, 492 (1991)

    work page 1991

  47. [47]

    Vahlbruch, M

    H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schn- abel, Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Pho- toelectric Quantum Efficiency, Phys. Rev. Lett.117, 110801 (2016)

    work page 2016

  48. [48]

    Miˇ cuda, I

    M. Miˇ cuda, I. Straka, M. Mikov´ a, M. Duˇ sek, N. J. Cerf, J. Fiur´ aˇ sek, and M. Jeˇ zek, Noiseless Loss Suppression in Quantum Optical Communication, Phys. Rev. Lett.109, 180503 (2012)

    work page 2012

  49. [49]

    C. M. Nunn, J. D. Franson, and T. B. Pittman, Herald- ing on the detection of zero photons, Phys. Rev. A104, 033717 (2021)

    work page 2021

  50. [50]

    T. C. Ralph and A. P. Lund, in Quantum Communica- tion Measurement and Computing edited by A. Lvovsky (AIP, New York, 2009), pp. 155–160

    work page 2009