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Quantum Optical Integrated Sensing and Communication with Homodyne BPSK Detection

Ioannis Krikidis

TL;DR

This work proposes a quantum optical ISAC framework (QISAC) that uses BPSK modulation and homodyne detection to jointly demodulate symbols and estimate an unknown channel phase rotation. The design minimizes the bit-error rate under a Fisher-information constraint on theta, realized via a two-loop algorithm: an inner EM loop for joint symbol detection and phase estimation at a fixed LO phase psi, and an outer loop that adaptively tunes psi to meet the sensing constraint. Closed-form expressions for BER and Fisher information establish the fundamental trade-off between communication reliability and sensing accuracy, with the LO phase aligning toward either communication or sensing optimization. Numerical results confirm rapid convergence, quantify the BER–sensing trade-off, and illustrate how system parameters like block length N and noise affect performance, highlighting the framework's practicality for quantum optical ISAC without claiming quantum advantage over classical ISAC.

Abstract

In this letter, we propose a quantum integrated sensing and communication scheme for a quantum optical link using binary phase-shift keying modulation and homodyne detection. The link operates over a phase-insensitive Gaussian channel with an unknown deterministic phase rotation, where the homodyne receiver jointly carries out symbol detection and phase estimation. We formulate a design problem that minimizes the bit-error rate subject to a Fisher information-based constraint on estimation accuracy. To solve it, we develop an iterative algorithm composed of an inner expectation-maximization loop for joint detection and estimation and an outer loop that adaptively retunes the local oscillator phase. Numerical results confirm the effectiveness of the proposed approach and demonstrate a fundamental trade-off between communication reliability and sensing accuracy.

Quantum Optical Integrated Sensing and Communication with Homodyne BPSK Detection

TL;DR

This work proposes a quantum optical ISAC framework (QISAC) that uses BPSK modulation and homodyne detection to jointly demodulate symbols and estimate an unknown channel phase rotation. The design minimizes the bit-error rate under a Fisher-information constraint on theta, realized via a two-loop algorithm: an inner EM loop for joint symbol detection and phase estimation at a fixed LO phase psi, and an outer loop that adaptively tunes psi to meet the sensing constraint. Closed-form expressions for BER and Fisher information establish the fundamental trade-off between communication reliability and sensing accuracy, with the LO phase aligning toward either communication or sensing optimization. Numerical results confirm rapid convergence, quantify the BER–sensing trade-off, and illustrate how system parameters like block length N and noise affect performance, highlighting the framework's practicality for quantum optical ISAC without claiming quantum advantage over classical ISAC.

Abstract

In this letter, we propose a quantum integrated sensing and communication scheme for a quantum optical link using binary phase-shift keying modulation and homodyne detection. The link operates over a phase-insensitive Gaussian channel with an unknown deterministic phase rotation, where the homodyne receiver jointly carries out symbol detection and phase estimation. We formulate a design problem that minimizes the bit-error rate subject to a Fisher information-based constraint on estimation accuracy. To solve it, we develop an iterative algorithm composed of an inner expectation-maximization loop for joint detection and estimation and an outer loop that adaptively retunes the local oscillator phase. Numerical results confirm the effectiveness of the proposed approach and demonstrate a fundamental trade-off between communication reliability and sensing accuracy.
Paper Structure (9 sections, 2 theorems, 19 equations, 4 figures, 1 algorithm)

This paper contains 9 sections, 2 theorems, 19 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Quantum integrated sensing and communication
  4. Inner loop (estimate $\theta$ and demodulate BPSK symbols for a given $\psi$)
  5. Outer loop (tuning of the LO phase $\psi$)
  6. Numerical results
  7. Conclusion
  8. Proof of proposition 1
  9. Proof of proposition 2

Key Result

Proposition 1

For BPSK transmitted coherent states and a homodyne receiver, the BER and the symbol Fisher information for the deterministic parameter $\theta$ are given by where $\mu'_m=-A\sin(\varphi_m+\phi)$. We also note that $F_c^{\max}=N\max_{\phi}F(\psi,\theta)$ which can be computed numerically (1-D search).

Figures (4)

  • Figure 1: Communication-sensing trade-off for BPSK with channel rotation $\theta=30^\circ$ and perturbation $\delta\theta=10^\circ$. The red axis ($\psi=\theta$) maximizes symbol separation and is communication-optimal, while the green axis ($\psi=\theta+\pi/2$) maximizes the projection shift due to $\delta\theta$ and is sensing-optimal. Dashed lines indicate the projections of the perturbed symbols onto each axis.
  • Figure 2: QISAC performance versus the number of iterations. (a) Estimated $\hat{\theta}$ (dashed: true $\theta=45^\circ$); (b) Fisher information (dashed: $\Gamma_{\min}=0.6F_c^{\max}$); (c) LO phase $\psi$; (d) BER: empirical (dashed: theory with $\phi=\theta-\hat{\psi}$). Setting: $N=1000$, and $\theta=45^\circ$.
  • Figure 3: QISAC performance versus the number of iterations. (a) Estimated $\hat{\theta}$ (dashed: true $\theta=60^\circ$); (b) Fisher information (dashed: $\Gamma_{\min}=0. 5F_c^{\max}$); (c) LO phase $\psi$; (d) BER: empirical (dashed: theory with $\phi=\theta-\hat{\psi}$). Setting: $N=500$, and $\theta=60^\circ$.
  • Figure 4: Tradeoff between communication performance (BER) and normalized estimation/sensing accuracy ($\Gamma_{\min}/F_c^{\max}$); simulation results (markers), theoretical results corresponding to known $\theta$ (dashed lines) . Setting: $\theta = 30^\circ$, $N_a \in \{1, 2,\,2.5,\,3\}$, $N \in \{5000,\,50000\}$.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof