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Quantum Rotation Diversity in Displaced Squeezed Binary Phase-Shift Keying

Ioannis Krikidis

TL;DR

This work tackles the reliability of quantum optical communications over Gamma-Gamma fading while preserving throughput by introducing quantum rotation diversity (QRD). QRD rotates pairs of consecutive BPSK-displaced squeezed states across two time slots and jointly detects with a maximum-likelihood receiver, achieving diversity gains without sacrificing spectral efficiency. At high photon numbers, the scheme delivers a diversity order of $d=4g$ (with $g=\min\{\epsilon,\zeta\}$) when $r>0$, and exhibits a super-diversity effect as displacement and squeezing scale with the total photon number $N$, yielding improved error performance compared to a no-rotation baseline. Numerical results validate the theory, showing substantial SER improvements and confirming the optimality of the rotation angle $\theta^{\star}=\tfrac{1}{2}\arctan(2)$ and energy split $\beta^{\star}=\tfrac{1}{2}$ in the asymptotic regime.

Abstract

We propose a quantum rotation diversity (QRD) scheme for optical quantum communication using binary phase-shift-keying displaced squeezed states and homodyne detection over Gamma-Gamma turbulence channels. Consecutive temporal modes are coupled by a passive orthogonal rotation that redistributes the displacement amplitude between slots, yielding a diversity order of two under independent fading and joint maximum-likelihood detection. Analytical expressions for the symbol-error rate performance, along with asymptotic results for the diversity and coding gains, are derived. The optimal rotation angle and energy allocation between displacement and squeezing are obtained in closed form. Furthermore, we show that when both the displacement amplitude and the squeezing strength scale with the total photon number, an effective diversity order of four is achieved. Numerical results validate the analysis and demonstrate the super-diversity behaviour of the proposed QRD scheme.

Quantum Rotation Diversity in Displaced Squeezed Binary Phase-Shift Keying

TL;DR

This work tackles the reliability of quantum optical communications over Gamma-Gamma fading while preserving throughput by introducing quantum rotation diversity (QRD). QRD rotates pairs of consecutive BPSK-displaced squeezed states across two time slots and jointly detects with a maximum-likelihood receiver, achieving diversity gains without sacrificing spectral efficiency. At high photon numbers, the scheme delivers a diversity order of (with ) when , and exhibits a super-diversity effect as displacement and squeezing scale with the total photon number , yielding improved error performance compared to a no-rotation baseline. Numerical results validate the theory, showing substantial SER improvements and confirming the optimality of the rotation angle and energy split in the asymptotic regime.

Abstract

We propose a quantum rotation diversity (QRD) scheme for optical quantum communication using binary phase-shift-keying displaced squeezed states and homodyne detection over Gamma-Gamma turbulence channels. Consecutive temporal modes are coupled by a passive orthogonal rotation that redistributes the displacement amplitude between slots, yielding a diversity order of two under independent fading and joint maximum-likelihood detection. Analytical expressions for the symbol-error rate performance, along with asymptotic results for the diversity and coding gains, are derived. The optimal rotation angle and energy allocation between displacement and squeezing are obtained in closed form. Furthermore, we show that when both the displacement amplitude and the squeezing strength scale with the total photon number, an effective diversity order of four is achieved. Numerical results validate the analysis and demonstrate the super-diversity behaviour of the proposed QRD scheme.
Paper Structure (12 sections, 2 theorems, 30 equations, 3 figures)

This paper contains 12 sections, 2 theorems, 30 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System model and the proposed QRD scheme
  3. Error probability and asymptotic analysis
  4. PEP and SER performance
  5. Asymptotic analysis
  6. Baseline (no rotation, single-slot)
  7. Numerical studies
  8. Conclusion
  9. Laplace transform of the Gamma--Gamma distribution
  10. Minimize PEP based on Laplace transformation properties
  11. Asymptotic expressions for high SNRs
  12. Diversity and coding gain

Key Result

Proposition 1

For the proposed QRD BPSK over i.i.d Gamma--Gamma fading with shapes $\epsilon,\zeta$ and $\epsilon\neq \zeta$, the optimal design that minimizes SER is attained at $\theta^\star=\frac{1}{2}\arctan(2)$, $r^\star=\tfrac{1}{2}\ln(2N+1)$, and $\alpha^\star=\sqrt{\tfrac{N(N+1)}{2N+1}}$. For the optimal

Figures (3)

  • Figure 1: System model of the proposed QRD-based quantum FSO communication scheme.
  • Figure 2: SER performance of QRD and baseline BPSK schemes versus the total mean photon number per symbol $N$; QRD uses an optimal angle $\theta^*=\frac{1}{2}\arctan(2)$.
  • Figure 3: SER performance of the proposed QRD scheme versus the rotation angle $\theta$ and the power split $\beta$; $N=80$ photons per symbol.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Theorem 1: High-SNR diversity and maximum coding gain
  • proof