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Applied Physics B

A quantum displacement receiver for coherent states modulated in polarization degree of freedom in photonic communications at 1550 nm

Francisco Javier Mendieta-Jiménez, Arturo Arvizu‐Mondragón, César A. López-Mercado, Ramón Muraoka-Espíritu

Published May 13, 2026• 0 citations
Publisher

Abstract

We present the theory and experimental realization of a quantum polarization-displacement receiver for photonic communications with laser coherent states modulated in their polarization degree of freedom, employing an unconditionally polarization-nulling photon counting scheme. We describe the quantum detection analysis for Polarization Shift Keying (PolSK) modulation formats with laser coherent states, deriving their theoretical performance bounds in error probability and mutual information; and we propose a receiver structure based on a polarization-displacement technique, inspired on the conventional quadrature-displacement schemes employed in the reception of Phase Shift Keying (PSK) modulation formats. Experimentally, we implement our coherent states receiver in a polarization-nulling configuration, employing linear optics for the polarization rotations and displacement, with photon counting at the telecommunications wavelength of 1550 nm, and performing post-detection count–to–voltage operations and logical decision with optimized photon number thresholds; additionally, as a reference, we also implement a quadrature-nulling receiver for a binary PSK format. We perform measurements on the symbol error probability of our receiver, as a function of the photon number of the received photonic signal, finding good agreement with the theoretical estimation at low photon numbers. This receiving structure has advantages over the conventional polarization-splitting and separate photon counting schemes, which is of interest in quantum communications, quantum cryptography and other fields in quantum information.

DOI
10.1007/s00340-026-08684-3

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We present the theory and experimental realization of a quantum polarization-displacement receiver for photonic communications with laser coherent states modulated in their polarization degree of freedom, employing an unconditionally polarization-nulling photon counting scheme. We describe the quantum detection analysis for Polarization Shift Keying (PolSK) modulation formats with laser coherent states, deriving their theoretical performance bounds in error probability and mutual information; and we propose a receiver structure based on a polarization-displacement technique, inspired on the conventional quadrature-displacement schemes employed in the reception of Phase Shift Keying (PSK) modulation formats. Experimentally, we implement our coherent states receiver in a polarization-nulling configuration, employing linear optics for the polarization rotations and displacement, with photon counting at the telecommunications wavelength of 1550 nm, and performing post-detection count–to–voltage operations and logical decision with optimized photon number thresholds; additionally, as a reference, we also implement a quadrature-nulling receiver for a binary PSK format. We perform measurements on the symbol error probability of our receiver, as a function of the photon number of the received photonic signal, finding good agreement with the theoretical estimation at low photon numbers. This receiving structure has advantages over the conventional polarization-splitting and separate photon counting schemes, which is of interest in quantum communications, quantum cryptography and other fields in quantum information.
Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing more complex quantum states such as squeezed-displaced states. One of the simplest receivers for state discrimination is the displacement receiver. However, our calculation demonstrates that when we use optimal parameters for a displacement receiver, squeezed-displaced states might not be necessary, and merely using coherent states suffice. We see no performance improvement in terms of probability of error of state discrimination as well as mutual information using displacement receivers when optimal squeezing parameters are used with squeezing operation on the transmitter side for BPSK and QPSK. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using squeezing operation on the receiver side just before detection provides an advantage in terms of increased mutual information for the low-photon regime compared to when no squeezing is used. For all other cases, squeezing offers no additional advantage.
An important problem in quantum information theory is finding the best possible performance of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing a number of quantum states such as coherent states and squeezed-displaced states. In this thesis, we provide optimal receiver design employing coherent states and squeezed-displaced states to maximize the mutual information and lower the error probability of state discrimination. In the case of pure coherent states, we derive an alternative channel capacity of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that the capacity is higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacements. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. We also explore the use of squeezing operations with a displacement receiver for state discrimination. Our calculation demonstrates that we see no performance improvement in terms of the probability of error of state discrimination or mutual information using displacement receivers when optimal squeezing on the transmitter side is used. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using the squeezing operation on the receiver side provides an advantage in terms of increased mutual information for the low-photon number regime compared to when no squeezing is used. In the later part of the thesis, we study entanglement-assisted communication using two-mode squeezing vacuum. The use of pre-shared entanglement in entanglement-assisted communication provides a superior alternative to classical communication specifically in the low brightness regime and highly noisy environment. In this thesis, we analyze the performance of a few low-complexity receivers that employ optical parametric amplifiers. In the simulation, we demonstrate that receiver designs with an entanglement-assisted scheme using phase-shift-keying modulation can outperform classical capacities. We describe a newly proposed 2x2 optical hybrid receiver for entanglement-assisted communication whose performance is roughly 10% better in terms of error probability as compared to previously proposed optical parametric amplifier-based receivers. Further, we find that using unequal priors for BPSK provides approximately three times the advantage over equal priors in terms of information rate.
The quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase-shift-keying coherent states in terms of average error rate and mutual information. Our receiver consists of on-off--type photon detectors and displacement operations without electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently available technology. For the quaternary signals feedforward operation is crucial to overcome the SQL with imperfect devices. We also analytically examine the asymptotic limit of the performance of the proposed receiver with respect to the number of feedforward steps.
An important problem in quantum information theory is finding the best possible capacity of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. In this paper, we derive an alternative channel capacity, CG, of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that CGis higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacement. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. Further, we present a comparative analysis of CGwith existing receiver designs. We extend our study to account for detector imperfections.imperfections.
This paper presents a practical optical communication framework that transmits binary information using distinct coherent states characterized by different mean photon numbers and detects the received signals via threshold-based photon counting. Unlike conventional approaches that often assume idealized detection environments, we rigorously analyze the performance of the proposed scheme under three realistic scenarios: (i) noise-free channels, (ii) channels impaired by additive Poisson noise, and (iii) turbulent free-space optical channels with fading and background noise. The coherent-state modulation enables energy-efficient transmission in the quantum-limited regime while the photon-counting receiver employs a statistically optimized decision threshold to discriminate between received photon-count levels. To address the lack of instantaneous channel state information in fading environments, we further propose a pilot-based channel estimation method that enables adaptive threshold selection. Closed-form expressions for decision thresholds and error probabilities are derived, and the effectiveness of the scheme is validated through detailed numerical simulations. These results offer design insights for photon-efficient, low-power optical communication systems operating under realistic physical impairments.
We implement the cyclic quantum receiver based on the theoretical proposal of Roy Bondurant and demonstrate experimentally below the shot-noise limit (SNL) discrimination of quadrature phase-shift keying signals (PSK). We also experimentally test the receiver generalized for longer communication alphabet lengths and coherent frequency shift keying (CFSK) encoding. Using off-the-shelf components, we obtain state discrimination error rates that are 3 dB and 4.6 dB below the SNLs of ideal classical receivers for quadrature PSK and CFSK encodings, respectively. The receiver unconditionally surpasses the SNL for M=8 PSK and CFSK. This receiver can be used for the simple and robust practical implementation of quantum-enhanced optical communication.