Practical quantum-enhanced receivers for classical communication

Abstract

Communication is an integral part of human life. Today, optical pulses are the preferred information carriers for long-distance communication. The exponential growth in data leads to a "capacity crunch" in the underlying physical systems. One of the possible methods to deter the exponential growth of physical resources for communication is to use quantum, rather than classical measurement at the receiver. Quantum measurement improves the energy efficiency of optical communication protocols by enabling discrimination of optical coherent states with the discrimination error rate below the shot-noise limit. In this review article, the authors focus on quantum receivers that can be practically implemented at the current state of technology, first and foremost displacement-based receivers. The authors present the experimentalist view on the progress in quantum-enhanced receivers and discuss their potential.

FIG. 1.

Classical and quantum limits to channel capacity

FIG. 2.

Resource use per bit for different communication protocols. Bandwidth and the theoretical minimum energy per bit requirements are shown for classical, quantum state discrimination of some communication protocols assuming a symbol error rate P = 10⁻⁵. The protocols with the same modulation method, but different alphabet lengths M are connected with colored lines. Power-limited protocols are above R/B = 1 line and bandwidth-limited protocols are below R/B = 1 line.

FIG. 3.

Binary phase shift keying constellation diagram.

FIG. 4.

M-ary phase shift keying constellation diagram example, M = 4.

FIG. 5.

M-ary pulse position modulation states, M = 4.

FIG. 6.

M-ary coherent frequency shift keying constellation diagram example, M = 4.

FIG. 7.

Classification of displacement-based quantum receivers. References to experimental demonstrations are in bold.

FIG. 8.

Schematic diagram of first quantum receivers for binary state discrimination. The displacement operation, $\widehat{D}$, uses a local oscillator state and a beam-splitter. (a) Kennedy-like receiver (non-adaptive) and (b) Dolinar-like receiver (with feedback).

FIG. 9.

Schematic diagram of modified Kennedy receivers. (a) Optimal displacement receiver (ODR) and (b) ODR with photon number resolution (PNR).

FIG. 10.

(a) Experimental scheme of CPN receiver for 4-ary PPM. (b) Decision strategy for 4-ary PPM. Broken arrows represent no photon detection and solid arrows represent photon detection after nulling. Green boxes are the received states after discrimination.

FIG. 11.

Schematic diagram of adaptive displacement receivers: (a) spatial adaptive displacement receiver and (b) temporal adaptive displacement receiver.

FIG. 12.

Time-resolving adaptive displacement receivers: (a) Bondurant/cyclic receiver and (b) time-resolving receiver with Bayesian inference.

FIG. 13.

(a) Binary signals optimized for communication in the channel with phase diffusion. Reprinted with permission from DiMario et al., npj Quantum Inf. 5, 65 (2019). Copyright 2019 Authors, licensed under a Creative Commons Attribution 4.0 International License; (b) displaced squeezed states (DSS) with opposite phases, as described in Ref. 79; (c) Wigner functions of single-rail qubit states, reproduced with permission from Izumi et al., J. Phys. B 51, 085502 (2018). Copyright 2018 IOP Publishing. All rights reserved.

FIG. 14.

Photon number distribution of single-rail qubits before and after displacement, reproduced with permission from Izumi et al., J. Phys. B 51, 085502 (2018). Copyright 2018 IOP Publishing. All rights reserved.

FIG. 15.

Potential improvement in resource use of quantum-enabled communication over classical technology. The classical resource use is comprised of shot-noise limits (at P_e = 10⁻⁵) for M-ary PSK (values above R/W = 1) and M-ary PPM (values below R/W = 1), red curve. The potential, but optimistic, quantum bound is Gordon capacity, black curve.