Probabilistic pulse-position modulation for classical communication on quantum channels

TL;DR

This paper introduces probabilistic pulse-position modulation (PPPM), a generalized coding scheme for quantum channels that distributes signals across multiple modes with optimized probabilities, outperforming traditional Hadamard codes in specific energy regimes.

Contribution

The paper proposes a novel PPPM scheme that generalizes Hadamard codes by distributing signals probabilistically across multiple modes, enhancing communication rates over quantum channels.

Findings

PPPM can outperform traditional Hadamard codes in intermediate energy regimes.

Derived an achievable communication rate for the proposed PPPM scheme.

Demonstrated the potential of mode-distributed coding strategies in quantum communication.

Abstract

Classical communication over lossy quantum channels is an essential topic in quantum information theory, with practical implications for optical-fiber and free-space communications. Multi-phase Hadamard codes, based on coherent-state Binary Phase-Shift Keying (BPSK) modulation and decoded using vacuum-or-pulse (VP) detectors, offer a promising approach for achieving high communication rates while relying only on linear optics and single-photon detectors (SPDs). However, their performance does not reach the ultimate Holevo limit. In this work, we propose a generalization of Hadamard codes that distributes the signal across multiple modes with optimized probabilities, rather than concentrating it in a single mode, dubbed probabilistic pulse-position modulation (PPPM). We derive an achievable communication rate, demonstrating that our PPPM can outperform traditional Hadamard codes in certain intermediate energy regimes.