Optimized communication strategies with binary coherent states over phase noise channels

The achievable rate of information transfer in optical communications is determined by the physical properties of the communication channel, such as the intrinsic channel noise. Bosonic phase noise channels, a class of non-Gaussian channels, have emerged as a relevant noise model in quantum information and optical communication. However, while the fundamental limits for communication over Gaussian channels have been extensively studied, the properties of communication over Bosonic phase noise channels are not well understood. Here we propose and demonstrate experimentally the concept of optimized communication strategies for communication over phase noise channels to enhance information transfer beyond what is possible with conventional methods of modulation and detection. Two key ingredients are generalized constellations of coherent states that interpolate between standard on-off keying and binary phase-shift keying formats, and non-Gaussian measurements based on photon number resolving detection of the coherently displaced signal. For a given power constraint and channel noise strength, these novel strategies rely on joint optimization of the input alphabet and the measurement to provide enhanced communication capability over a non-Gaussian channel characterized in terms of the error rate as well as mutual information.

[1]  H. Bechmann-Pasquinucci,et al.  Quantum cryptography , 2001, quant-ph/0101098.

[2]  P. J. Clarke,et al.  Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light , 2012, Nature communications.

[3]  Juan Miguel Arrazola,et al.  Practical quantum retrieval games , 2016 .

[4]  Masahiro Takeoka,et al.  QPSK coherent state discrimination via a hybrid receiver , 2012, 1204.0888.

[5]  F. E. Becerra,et al.  Photon number resolution enables quantum receiver for realistic coherent optical communications , 2014, Nature Photonics.

[6]  Ivan B. Djordjevic,et al.  A survey on recent advances in optical communications , 2014, Comput. Electr. Eng..

[7]  R. Bondurant,et al.  Near-quantum optimum receivers for the phase-quadrature coherent-state channel. , 1993, Optics letters.

[8]  Masahide Sasaki,et al.  Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers , 2007, 0706.1038.

[9]  M T DiMario,et al.  Robust Measurement for the Discrimination of Binary Coherent States. , 2018, Physical review letters.

[10]  Julius Goldhar,et al.  Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination , 2013, Nature Photonics.

[11]  Feihu Xu,et al.  Observation of Quantum Fingerprinting Beating the Classical Limit. , 2016, Physical review letters.

[12]  S. Guha,et al.  Fundamental rate-loss tradeoff for optical quantum key distribution , 2014, Nature Communications.

[13]  U. Andersen,et al.  Discrimination of optical coherent states using a photon number resolving detector , 2009, 0905.2496.

[14]  Fred Daneshgaran,et al.  Soft-Metric-Based Channel Decoding for Photon Counting Receivers , 2014, IEEE Journal of Selected Topics in Quantum Electronics.

[15]  N. Cerf,et al.  Quantum key distribution using gaussian-modulated coherent states , 2003, Nature.

[16]  S. Olivares,et al.  Squeezing-Enhanced Phase-Shift-Keyed Binary Communication in Noisy Channels , 2017, Proceedings.

[17]  Masahiro Takeoka,et al.  Demonstration of coherent-state discrimination using a displacement-controlled photon-number-resolving detector. , 2009, Physical review letters.

[18]  Saikat Guha,et al.  Realizable receivers for discriminating coherent and multicopy quantum states near the quantum limit , 2012, 1212.2048.

[19]  U. Andersen,et al.  Quadrature phase shift keying coherent state discrimination via a hybrid receiver , 2012 .

[20]  Homodyne-like detection for coherent state-discrimination in the presence of phase noise. , 2016, Optics express.

[21]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[22]  Matteo G. A. Paris,et al.  Noisy quantum phase communication channels , 2015 .

[23]  Christoph Marquardt,et al.  A robust quantum receiver for phase shift keyed signals , 2014, 1412.6242.

[24]  K. Banaszek,et al.  Dephasing in coherent communication with weak signal states , 2013, 1307.6871.

[25]  Charles H. Bennett,et al.  Quantum cryptography using any two nonorthogonal states. , 1992, Physical review letters.

[26]  Marco G. Genoni,et al.  Optical interferometry in the presence of large phase diffusion , 2012, 1203.2956.

[27]  Saikat Guha,et al.  Structured optical receivers to attain superadditive capacity and the Holevo limit , 2011, Physical review letters.

[28]  C. Helstrom Quantum detection and estimation theory , 1969 .

[29]  Juan Miguel Arrazola,et al.  Experimental quantum fingerprinting with weak coherent pulses , 2015, Nature Communications.

[30]  Kazuro Kikuchi,et al.  Fundamentals of Coherent Optical Fiber Communications , 2016, Journal of Lightwave Technology.

[31]  Stefano Olivares,et al.  Optical phase estimation in the presence of phase diffusion. , 2010, Physical review letters.

[32]  A. Holevo,et al.  Ultimate classical communication rates of quantum optical channels , 2014, Nature Photonics.

[33]  Juan Miguel Arrazola,et al.  Quantum communication with coherent states and linear optics , 2014, 1406.7189.

[34]  S. Olivares,et al.  Quantum phase communication channels in the presence of static and dynamical phase diffusion , 2015, 1505.03160.

[35]  Matteo G. A. Paris,et al.  Displacement operator by beam splitter , 1996 .

[36]  Masahide Sasaki,et al.  Demonstration of near-optimal discrimination of optical coherent states. , 2008, Physical review letters.

[37]  A. Holevo,et al.  Quantum state majorization at the output of bosonic Gaussian channels , 2013, Nature Communications.

[38]  Robert L. Cook,et al.  Optical coherent state discrimination using a closed-loop quantum measurement , 2007, Nature.

[39]  Masahide Sasaki,et al.  Quantum receivers with squeezing and photon-number-resolving detectors for M -ary coherent state discrimination , 2013, 1302.2691.

[40]  Se-Wan Ji,et al.  Gaussian benchmark for optical communication aiming towards ultimate capacity , 2016, 1606.00962.

[41]  Matteo G. A. Paris,et al.  Homodyne detection as a near-optimum receiver for phase-shift-keyed binary communication in the presence of phase diffusion , 2013, 1305.4201.

[42]  P. Grangier,et al.  Continuous variable quantum cryptography using coherent states. , 2001, Physical review letters.

[43]  Alexandre Graell i Amat,et al.  Design of APSK Constellations for Coherent Optical Channels with Nonlinear Phase Noise , 2013, IEEE Transactions on Communications.

[44]  A. R. Ferdinand,et al.  Multi-state discrimination below the quantum noise limit at the single-photon level , 2017, 1711.00074.

[45]  Gisin,et al.  Quantum cryptography with coherent states. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[46]  J. Kahn,et al.  Signal Design and Detection in Presence of Nonlinear Phase Noise , 2007, Journal of Lightwave Technology.

[47]  Seth Lloyd,et al.  Explicit capacity-achieving receivers for optical communication and quantum reading , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[48]  M. T. DiMario,et al.  Implementation of a single-shot receiver for quaternary phase-shift keyed coherent states , 2018, 1803.07209.

[49]  Masahide Sasaki,et al.  Quantum receiver beyond the standard quantum limit of coherent optical communication. , 2011, Physical review letters.

[50]  S. Lloyd,et al.  Classical capacity of the lossy bosonic channel: the exact solution. , 2003, Physical review letters.

[51]  L. Banchi,et al.  Fundamental limits of repeaterless quantum communications , 2015, Nature Communications.

[52]  M. Paris,et al.  Phase noise in collective binary phase shift keying with Hadamard words. , 2015, Optics express.

[53]  Alan Pak Tao Lau,et al.  Coherent detection in optical fiber systems. , 2008, Optics express.

[54]  Peter J. Winzer,et al.  Roadmap on Optical Communications , 2016 .

[55]  G. Leuchs,et al.  Coherent state quantum key distribution with multi letter phase-shift keying , 2009, 0902.1895.

[56]  G Leuchs,et al.  Continuous variable quantum cryptography: beating the 3 dB loss limit. , 2002, Physical review letters.

[57]  Julius Goldhar,et al.  M-ary-state phase-shift-keying discrimination below the homodyne limit , 2011 .

[58]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..