Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Active Hypothesis Testing for Quantum Detection of Phase-Shift Keying Coherent States

Yun-Feng Lo, Matthieu R. Bloch

TL;DR

This work addresses quantum detection of PSK-coded coherent states under resource constraints and dark counts by formulating the problem as active hypothesis testing with a Dolinar-like receiver. It derives an energy-aware open-loop error exponent $\beta_{OL}$ that optimizes over constrained input distributions and a Chernoff-type divergence between Poisson-observation models, providing a bound $P_e \le (|\mathcal{M}|-1)\exp(-\alpha^2\beta_{OL})$. In the binary case, the authors identify regimes where time-sharing between the zero displacement and Kennedy displacement is optimal at high SNR, while showing that such a policy need not always be exponent-optimal. Simulations demonstrate practical gains over homodyne detection and competitive performance relative to Helstrom limits, validating the active hypothesis testing framework for designing resource-constrained quantum receivers.

Abstract

This paper explores the quantum detection of Phase-Shift Keying (PSK)-coded coherent states through the lens of active hypothesis testing, focusing on a Dolinar-like receiver with constraints on displacement amplitude and energy. With coherent state slicing, we formulate the problem as a controlled sensing task in which observation kernels have parameters shrinking with sample size. The constrained open-loop error exponent and a corresponding upper bound on the Bayesian error probability are proven. Surprisingly, the exponent-optimal open-loop policy for binary PSK with high dark counts is not simply time-sharing. This work serves as a first step towards obtaining analytical insights through the active hypothesis testing framework for designing resource-constrained quantum communication receivers.

Active Hypothesis Testing for Quantum Detection of Phase-Shift Keying Coherent States

TL;DR

This work addresses quantum detection of PSK-coded coherent states under resource constraints and dark counts by formulating the problem as active hypothesis testing with a Dolinar-like receiver. It derives an energy-aware open-loop error exponent that optimizes over constrained input distributions and a Chernoff-type divergence between Poisson-observation models, providing a bound . In the binary case, the authors identify regimes where time-sharing between the zero displacement and Kennedy displacement is optimal at high SNR, while showing that such a policy need not always be exponent-optimal. Simulations demonstrate practical gains over homodyne detection and competitive performance relative to Helstrom limits, validating the active hypothesis testing framework for designing resource-constrained quantum receivers.

Abstract

This paper explores the quantum detection of Phase-Shift Keying (PSK)-coded coherent states through the lens of active hypothesis testing, focusing on a Dolinar-like receiver with constraints on displacement amplitude and energy. With coherent state slicing, we formulate the problem as a controlled sensing task in which observation kernels have parameters shrinking with sample size. The constrained open-loop error exponent and a corresponding upper bound on the Bayesian error probability are proven. Surprisingly, the exponent-optimal open-loop policy for binary PSK with high dark counts is not simply time-sharing. This work serves as a first step towards obtaining analytical insights through the active hypothesis testing framework for designing resource-constrained quantum communication receivers.

Paper Structure

This paper contains 8 sections, 2 theorems, 92 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Notations
  3. Problem setting
  4. Main results
  5. Theoretical results
  6. Simulation results
  7. Proof of Theorem \ref{['thm:char']}
  8. Proof of Proposition \ref{['prop:policy']}

Key Result

Theorem 4.1

Given $R_\textnormal{SN}$, $R_\textnormal{CA}$ and $R_\textnormal{CE}$, the optimal amplitude and average energy constrained open-loop error exponent w.r.t. $n_\textnormal{s}=\alpha^2$ can be characterized as where for each $v\in\mathbb{C}$ and $m\in\mathcal{M}$, we define the distribution $P_m^v \triangleq \textnormal{Poi}(\Lambda_m^v)$ with the rate $\Lambda_m^v \triangleq \Lambda_m(v) \triangl

Figures (7)

  • Figure 1: Sequential detection of optical quantum states. Adapted from chung_capacity_2017.
  • Figure 2: Temporal slicing of the input coherent state pulse with total duration $T$ and constant amplitude $A$ into $N$ slices, each of duration $\Delta = T / N$.
  • Figure 3: A control signal of duration $T$ and generally non-constant amplitudes across $N$ intervals of duration $\Delta$.
  • Figure 4: Probability of error versus $\alpha^2$. Parameter values are $R_\textnormal{SN}=10^{6}$ ($r_\textnormal{SN}=10^{-6}$), $R_\textnormal{CA}=1$ and $R_\textnormal{CE}=1$.
  • Figure 5: Probability of error versus $\alpha^2$. Parameter values are $R_\textnormal{SN}=10^{2}$ ($r_\textnormal{SN}=10^{-2}$), $R_\textnormal{CA}=1$ and $R_\textnormal{CE}=1$.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Theorem 4.1
  • proof
  • Proposition 4.2
  • proof