Generative Data Intelligence

Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination

Date:

Jasminder S. Sidhu1, Michael S. Bullock2, Saikat Guha2,3, and Cosmo Lupo4,5

1SUPA Department of Physics, The University of Strathclyde, Glasgow, G4 0NG, UK
2Department of Electrical and Computer Engineering, The University of Arizona, Tucson, Arizona 85721, USA
3College of Optical Sciences, The University of Arizona, Tucson, Arizona 85721, USA
4Dipartimento Interateneo di Fisica, Politecnico & Università di Bari, 70126 Bari, Italy
5INFN, Sezione di Bari, 70126 Bari, Italy

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are prime candidates as information carriers for optical communications. A large body of literature exists on their quantum-limited estimation and discrimination. However, very little is known about the practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and outline a theory of USD with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, auxiliary vacuum modes, and on-off photon detection. Our results indicate that, in some regimes, these currently-available optical components are typically sufficient to achieve near-optimal unambiguous discrimination of multiple, multimode coherent states.

Quantum-enhanced receivers are in the vanguard of new quantum technologies. For applications in optical communications, they provide improved discriminatory capabilities for multiple non-orthogonal quantum states. This is particularly important for weak coherent state alphabets given their pivotal role as information carriers in quantum sensing, communication, and computing. A well-designed quantum receiver combines practicality with high performance, where the latter is quantified through a suitable task-dependent figure of merit Within the framework of unambiguous state discrimination (USD), quantum receivers are designed to identify an unknown state without error and its performance is benchmarked in terms of the minimum average probability of obtaining an inconclusive event.

There is a wide body of literature devoted to establishing the global bound for USD for different families of quantum states, including semidefinite programming and even exact analytical solution where symmetry in the states permit. These approaches provide formal mathematical descriptions for globally optimal USD measurements but fall short of providing an explicit or feasible receiver construction. Surprisingly, very little is known about practical USD receivers for coherent states beyond phase-shift keying constellations, and whether they can achieve the global bounds.

To close this gap, we establish a new theory for USD that operates under practical measurement schemes. In particular, our receivers leverage only limited resources, such as multi-mode linear passive optics, phase-space displacement operations, auxiliary vacuum modes, and mode-wise on-off photon detection. We develop multiple classes of receivers, each suited to specific properties of the coherent state constellation. We apply our theory to a number of coherent-state modulations and benchmark the performance to existing global bounds on USD. We demonstrate that in some regimes this practical, yet restricted, set of physical operations is typically sufficient to deliver near-optimal performance. This work establishes a theoretical framework to understand and master the design of receivers to enable near-optimal USD of coherent states.

â–º BibTeX data

â–º References

[1] Charles H. Bennett, Gilles Brassard, and N. David Mermin, Quantum cryptography without bell’s theorem, Phys. Rev. Lett. 68, 557 (1992).
https:/​/​doi.org/​10.1103/​PhysRevLett.68.557

[2] Jasminder S. Sidhu and Pieter Kok, Geometric perspective on quantum parameter estimation, AVS Quantum Science 2, 014701 (2020).
https:/​/​doi.org/​10.1116/​1.5119961

[3] Jasminder S. Sidhu and Pieter Kok, Quantum fisher information for general spatial deformations of quantum emitters, ArXiv (2018), https:/​/​doi.org/​10.48550/​arXiv.1802.01601, arXiv:1802.01601 [quant-ph].
https:/​/​doi.org/​10.48550/​arXiv.1802.01601
arXiv:1802.01601

[4] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, et al., Advances in quantum cryptography, Adv. Opt. Photon. 12, 1012 (2020).
https:/​/​doi.org/​10.1364/​AOP.361502

[5] Jasminder S. Sidhu, Siddarth K. Joshi, Mustafa Gündoğan, Thomas Brougham, David Lowndes, Luca Mazzarella, Markus Krutzik, Sonali Mohapatra, Daniele Dequal, Giuseppe Vallone, et al., Advances in space quantum communications, IET Quantum Communication , 1 (2021a).
https:/​/​doi.org/​10.1049/​qtc2.12015

[6] S. Schaal, I. Ahmed, J. A. Haigh, L. Hutin, B. Bertrand, S. Barraud, M. Vinet, C.-M. Lee, N. Stelmashenko, J. W. A. Robinson, et al., Fast gate-based readout of silicon quantum dots using josephson parametric amplification, Phys. Rev. Lett. 124, 067701 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.067701

[7] Joonwoo Bae and Leong-Chuan Kwek, Quantum state discrimination and its applications, J. Phys. A: Math. Theoret. 48, 083001 (2015).
https:/​/​doi.org/​10.1088/​1751-8113/​48/​8/​083001

[8] I. A. Burenkov, M. V. Jabir, and S. V. Polyakov, Practical quantum-enhanced receivers for classical communication, AVS Quantum Science 3 (2021), https:/​/​doi.org/​10.1116/​5.0036959.
https:/​/​doi.org/​10.1116/​5.0036959

[9] Ivan A. Burenkov, N. Fajar R. Annafianto, M. V. Jabir, Michael Wayne, Abdella Battou, and Sergey V. Polyakov, Experimental shot-by-shot estimation of quantum measurement confidence, Phys. Rev. Lett. 128, 040404 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.128.040404

[10] Hemani Kaushal and Georges Kaddoum, Optical communication in space: Challenges and mitigation techniques, IEEE Communications Surveys & Tutorials 19, 57 (2017).
https:/​/​doi.org/​10.1109/​COMST.2016.2603518

[11] E. C. G. Sudarshan, Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams, Phys. Rev. Lett. 10, 277 (1963).
https:/​/​doi.org/​10.1103/​PhysRevLett.10.277

[12] Roy J. Glauber, Coherent and incoherent states of the radiation field, Phys. Rev. 131, 2766 (1963).
https:/​/​doi.org/​10.1103/​PhysRev.131.2766

[13] I. D. Ivanovic, How to differentiate between non-orthogonal states, Phys. Lett. A 123, 257 (1987).
https:/​/​doi.org/​10.1016/​0375-9601(87)90222-2

[14] D. Dieks, Overlap and distinguishability of quantum states, Phys. Lett. A 126, 303 (1988).
https:/​/​doi.org/​10.1016/​0375-9601(88)90840-7

[15] Asher Peres and Daniel R Terno, Optimal distinction between non-orthogonal quantum states, J. Phys. A: Math. Gen. 31, 7105 (1998).
https:/​/​doi.org/​10.1088/​0305-4470/​31/​34/​013

[16] Y.C. Eldar, A semidefinite programming approach to optimal unambiguous discrimination of quantum states, IEEE Transactions on Information Theory 49, 446 (2003).
https:/​/​doi.org/​10.1109/​TIT.2002.807291

[17] Anthony Chefles, Unambiguous discrimination between linearly independent quantum states, Physics Letters A 239, 339 (1998).
https:/​/​doi.org/​10.1016/​S0375-9601(98)00064-4

[18] Gael Sentís, John Calsamiglia, and Ramon Muñoz Tapia, Exact identification of a quantum change point, Phys. Rev. Lett. 119, 140506 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.140506

[19] Kenji Nakahira, Kentaro Kato, and Tsuyoshi Sasaki Usuda, Local unambiguous discrimination of symmetric ternary states, Phys. Rev. A 99, 022316 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.99.022316

[20] Gael Sentís, Esteban Martínez-Vargas, and Ramon Muñoz-Tapia, Online identification of symmetric pure states, Quantum 6, 658 (2022).
https:/​/​doi.org/​10.22331/​q-2022-02-21-658

[21] Yuqing Sun, Mark Hillery, and János A. Bergou, Optimum unambiguous discrimination between linearly independent nonorthogonal quantum states and its optical realization, Phys. Rev. A 64, 022311 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.64.022311

[22] János A. Bergou, Ulrike Futschik, and Edgar Feldman, Optimal unambiguous discrimination of pure quantum states, Phys. Rev. Lett. 108, 250502 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.250502

[23] H. Yuen, R. Kennedy, and M. Lax, Optimum testing of multiple hypotheses in quantum detection theory, IEEE Trans. Inf. Theory 21, 125 (1975).
https:/​/​doi.org/​10.1109/​TIT.1975.1055351

[24] Carl W. Helstrom, Quantum Detection and Estimation Theory (Academic Press Inc., 1976).

[25] B. Huttner, N. Imoto, N. Gisin, and T. Mor, Quantum cryptography with coherent states, Phys. Rev. A 51, 1863 (1995).
https:/​/​doi.org/​10.1103/​PhysRevA.51.1863

[26] Konrad Banaszek, Optimal receiver for quantum cryptography with two coherent states, Phys. Lett. A 253, 12 (1999).
https:/​/​doi.org/​10.1016/​S0375-9601(99)00015-8

[27] S. J. van Enk, Unambiguous state discrimination of coherent states with linear optics: Application to quantum cryptography, Phys. Rev. A 66, 042313 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.66.042313

[28] Miloslav Dušek, Mika Jahma, and Norbert Lütkenhaus, Unambiguous state discrimination in quantum cryptography with weak coherent states, Phys. Rev. A 62, 022306 (2000).
https:/​/​doi.org/​10.1103/​PhysRevA.62.022306

[29] Patrick J. Clarke, Robert J. Collins, Vedran Dunjko, Erika Andersson, John Jeffers, and Gerald S. Buller, Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light, Nat. Commun. 3, 1174 (2012).
https:/​/​doi.org/​10.1038/​ncomms2172

[30] F. E. Becerra, J. Fan, and A. Migdall, Implementation of generalized quantum measurements for unambiguous discrimination of multiple non-orthogonal coherent states, Nat. Commun. 4, 2028 (2013).
https:/​/​doi.org/​10.1038/​ncomms3028

[31] Shuro Izumi, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen, Tomography of a feedback measurement with photon detection, Phys. Rev. Lett. 124, 070502 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.070502

[32] Shuro Izumi, Jonas S. Neergaard-Nielsen, and Ulrik L. Andersen, Adaptive generalized measurement for unambiguous state discrimination of quaternary phase-shift-keying coherent states, PRX Quantum 2, 020305 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.020305

[33] M. T. DiMario and F. E. Becerra, Demonstration of optimal non-projective measurement of binary coherent states with photon counting, npj Quantum Inf 8, 84 (2022).
https:/​/​doi.org/​10.1038/​s41534-022-00595-3

[34] M Takeoka, H Krovi, and S Guha, Achieving the holevo capacity of a pure state classical-quantum channel via unambiguous state discrimination, in 2013 IEEE International Symposium on Information Theory (2013) pp. 166–170.

[35] A.S. Holevo, The capacity of the quantum channel with general signal states, IEEE Trans. Inf. Theory 44, 269 (1998).
https:/​/​doi.org/​10.1109/​18.651037

[36] Saikat Guha, Structured optical receivers to attain superadditive capacity and the holevo limit, Phys. Rev. Lett. 106, 240502 (2011a).
https:/​/​doi.org/​10.1103/​PhysRevLett.106.240502

[37] S Guha, Z Dutton, and J H Shapiro, On quantum limit of optical communications: Concatenated codes and joint-detection receivers, in 2011 IEEE International Symposium on Information Theory Proceedings (2011) pp. 274–278.

[38] Matteo Rosati, Andrea Mari, and Vittorio Giovannetti, Multiphase hadamard receivers for classical communication on lossy bosonic channels, Phys. Rev. A 94, 062325 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.94.062325

[39] Christoffer Wittmann, Ulrik L. Andersen, Masahiro Takeoka, Denis Sych, and Gerd Leuchs, Demonstration of coherent-state discrimination using a displacement-controlled photon-number-resolving detector, Phys. Rev. Lett. 104, 100505 (2010a).
https:/​/​doi.org/​10.1103/​PhysRevLett.104.100505

[40] Christoffer Wittmann, Ulrik L. Andersen, Masahiro Takeoka, Denis Sych, and Gerd Leuchs, Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector, Phys. Rev. A 81, 062338 (2010b).
https:/​/​doi.org/​10.1103/​PhysRevA.81.062338

[41] B. Huttner, A. Muller, J. D. Gautier, H. Zbinden, and N. Gisin, Unambiguous quantum measurement of nonorthogonal states, Phys. Rev. A 54, 3783 (1996).
https:/​/​doi.org/​10.1103/​PhysRevA.54.3783

[42] Roger B. M. Clarke, Anthony Chefles, Stephen M. Barnett, and Erling Riis, Experimental demonstration of optimal unambiguous state discrimination, Phys. Rev. A 63, 040305 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.63.040305

[43] Alessandro Ferraro, Stefano Olivares, and Matteo G. A. Paris, Gaussian states in continuous variable quantum information (Bibliopolis (Napoli), 2005) arXiv:quant-ph/​0503237.
https:/​/​doi.org/​10.48550/​arXiv.quant-ph/​0503237
arXiv:quant-ph/0503237

[44] P. Aniello, C. Lupo, and M. Napolitano, Exploring representation theory of unitary groups via linear optical passive devices, Open Systems & Information Dynamics 13, 415 (2006).
https:/​/​doi.org/​10.1007/​s11080-006-9023-1

[45] Scott Aaronson and Alex Arkhipov, The computational complexity of linear optics, in Proceedings of the forty-third annual ACM symposium on Theory of computing (ACM, 2011) pp. 333–342.
https:/​/​doi.org/​10.1145/​1993636.1993682

[46] Michael Reck, Anton Zeilinger, Herbert J. Bernstein, and Philip Bertani, Experimental realization of any discrete unitary operator, Phys. Rev. Lett. 73, 58 (1994).
https:/​/​doi.org/​10.1103/​PhysRevLett.73.58

[47] William R. Clements, Peter C. Humphreys, Benjamin J. Metcalf, W. Steven Kolthammer, and Ian A. Walmsley, Optimal design for universal multiport interferometers, Optica 3, 1460 (2016).
https:/​/​doi.org/​10.1364/​OPTICA.3.001460

[48] B. A. Bell and I. A. Walmsley, Further compactifying linear optical unitaries, APL Photonics 6, 070804 (2021).
https:/​/​doi.org/​10.1063/​5.0053421

[49] Jasminder S. Sidhu, Shuro Izumi, Jonas S. Neergaard-Nielsen, Cosmo Lupo, and Ulrik L. Andersen, Quantum receiver for phase-shift keying at the single-photon level, PRX Quantum 2, 010332 (2021b).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010332

[50] Saikat Guha, Patrick Hayden, Hari Krovi, Seth Lloyd, Cosmo Lupo, Jeffrey H. Shapiro, Masahiro Takeoka, and Mark M. Wilde, Quantum enigma machines and the locking capacity of a quantum channel, Phys. Rev. X 4, 011016 (2014).
https:/​/​doi.org/​10.1103/​PhysRevX.4.011016

[51] M. Skotiniotis, R. Hotz, J. Calsamiglia, and R. Muñoz-Tapia, Identification of malfunctioning quantum devices, arXiv:1808.02729 (2018), https:/​/​doi.org/​10.48550/​arXiv.1808.02729, arXiv:arXiv:1808.02729.
https:/​/​doi.org/​10.48550/​arXiv.1808.02729
arXiv:arXiv:1808.02729

[52] Bobak Nazer and Michael Gastpar, The case for structured random codes in network capacity theorems, European Transactions on Telecommunications 19, 455 (2008).
https:/​/​doi.org/​10.1002/​ett.1284

[53] Saikat Guha, Structured optical receivers to attain superadditive capacity and the holevo limit, Phys. Rev. Lett. 106, 240502 (2011b).
https:/​/​doi.org/​10.1103/​PhysRevLett.106.240502

[54] Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, 2nd ed., Vol. 11 (Wiley-Interscience, 2006).

[55] Yury Polyanskiy, H. Vincent Poor, and Sergio Verdu, Channel coding rate in the finite blocklength regime, IEEE Transactions on Information Theory 56, 2307 (2010).
https:/​/​doi.org/​10.1109/​TIT.2010.2043769

[56] Si-Hui Tan, Zachary Dutton, Ranjith Nair, and Saikat Guha, Finite codelength analysis of the sequential waveform nulling receiver for m-ary psk, in 2015 IEEE International Symposium on Information Theory (ISIT) (2015) pp. 1665–1670.
https:/​/​doi.org/​10.1109/​ISIT.2015.7282739

[57] Mankei Tsang, Poisson quantum information, Quantum 5, 527 (2021).
https:/​/​doi.org/​10.22331/​q-2021-08-19-527

[58] Krishna Kumar Sabapathy and Andreas Winter, Bosonic data hiding: power of linear vs non-linear optics, arXiv:2102.01622 (2021), https:/​/​doi.org/​10.48550/​arXiv.2102.01622, arXiv:arXiv:2102.01622.
https:/​/​doi.org/​10.48550/​arXiv.2102.01622
arXiv:arXiv:2102.01622

[59] Ludovico Lami, Quantum data hiding with continuous variable systems, Phys. Rev. A 104, 052428 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.104.052428

Cited by

[1] Alessio Belenchia, Matteo Carlesso, Ömer Bayraktar, Daniele Dequal, Ivan Derkach, Giulio Gasbarri, Waldemar Herr, Ying Lia Li, Markus Rademacher, Jasminder Sidhu, Daniel K. L. Oi, Stephan T. Seidel, Rainer Kaltenbaek, Christoph Marquardt, Hendrik Ulbricht, Vladyslav C. Usenko, Lisa Wörner, André Xuereb, Mauro Paternostro, and Angelo Bassi, “Quantum physics in space”, Physics Reports 951, 1 (2022).

[2] Jasminder S. Sidhu, Thomas Brougham, Duncan McArthur, Roberto G. Pousa, and Daniel K. L. Oi, “Finite key effects in satellite quantum key distribution”, npj Quantum Information 8, 18 (2022).

[3] M. T. DiMario and F. E. Becerra, “Demonstration of optimal non-projective measurement of binary coherent states with photon counting”, npj Quantum Information 8, 84 (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-05-31 14:14:17). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-05-31 14:14:16: Could not fetch cited-by data for 10.22331/q-2023-05-31-1025 from Crossref. This is normal if the DOI was registered recently.

spot_img

Latest Intelligence

spot_img

Chat with us

Hi there! How can I help you?