Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector

Phase estimation represents a crucial challenge in many fields of Physics, ranging from Quantum Metrology to Quantum Information Processing. This task is usually pursued by means of interferometric schemes, in which the choice of the input states and of the detection apparatus is aimed at minimizing the uncertainty in the estimation of the relative phase between the inputs. State discrimination protocols in communication channels with coherent states also require the monitoring of the optical phase. Therefore, the problem of phase estimation is relevant to face the issue of coherent states discrimination. Here we consider a quasi-optimal Kennedy-like receiver, based on the interference of two coherent signals, to be discriminated, with a reference local oscillator. By means of the Bayesian processing of a small amount of data drawn from the outputs of the shot-by-shot discrimination protocol, we demonstrate the achievement of the minimum uncertainty in phase estimation, also in the presence of uniform phase noise. Moreover, we show that the use of photon-number resolving detectors in the receiver improves the phase-estimation strategy, especially with respect to the usually employed on/off detectors. From the experimental point of view, this comparison is realized by employing hybrid photodetectors.

[1]  M. Paris.  Quantum estimation for quantum technology , 2008, 0804.2981.

[2]  R. Filip,et al.  Probabilistic Cloning of Coherent States without a Phase Reference , 2011, 1108.4241.

[3]  Claudia Biermann,et al.  Mathematical Methods Of Statistics , 2016 .

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

[5]  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.

[6]  Gianfranco Cariolaro,et al.  Performance of quantum data transmission systems in the presence of thermal noise , 2010, IEEE Transactions on Communications.

[7]  Matteo G. A. Paris,et al.  Binary optical communication in single-mode and entangled quantum noisy channels , 2003 .

[8]  Matteo G. A. Paris,et al.  Bayesian estimation in homodyne interferometry , 2009, 0901.2585.

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

[10]  A. Andreoni,et al.  Self-consistent characterization of light statistics , 2008, 0810.4055.

[11]  A. Andreoni,et al.  Light statistics by non-calibrated linear photodetectors , 2008, 0810.4026.

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

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

[14]  H. Cramér.  Mathematical Methods of Statistics (PMS-9), Volume 9 , 1946 .

[15]  James D. Franson,et al.  Quantum communications , 2020, Advanced Sciences and Technologies for Security Applications.

[16]  Joanne M. Morrisey,et al.  Branched Tricarboxylic Acid Metabolism in Plasmodium falciparum , 2010, Nature.

[17]  Antonio Assalini,et al.  Revisiting the Dolinar receiver through multiple-copy state discrimination theory , 2011, 1107.5452.

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

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

[20]  A. Andreoni,et al.  Self-consistent phase determination for Wigner function reconstruction , 2009, 0909.3726.

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

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

[23]  Masahiro Takeoka,et al.  Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector , 2010, 1002.0232.

[24]  Masahide Sasaki,et al.  Displacement receiver for phase-shift-keyed coherent states , 2012, 1208.1815.

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

[26]  JM Geremia.  Distinguishing between optical coherent states with imperfect detection (9 pages) , 2004 .

[27]  Maria Bondani,et al.  Bracket states for communication protocols with coherent states , 2014 .

[28]  Sam Dolinar,et al.  Binary quantum receiver concept demonstration , 2006, SPIE LASE.

[29]  Matteo G. A. Paris,et al.  Drawbacks of the use of fidelity to assess quantum resources , 2013, 1309.5325.

[30]  M. G. A. Paris,et al.  Optimal estimation of joint parameters in phase space , 2012, 1206.4867.

[31]  Stefano Olivares,et al.  Bayesian estimation of one-parameter qubit gates , 2008, 0812.0923.

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