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Optics Letters

Photon-correlation-enhanced capacity in a noisy low-photon-rate PPM photon-counting channel

Zhichao Jiang, Qihang Liu, Jung‐Tsung Shen

Published May 13, 2026• 0 citations
Publisher

Abstract

This work investigates the enhancement of channel capacity in photon-starved deep-space optical links by leveraging inter-photon correlations. We analyze an M-ary pulse-position modulation (PPM) photon-counting channel in the presence of Poisson background noise and compare conventional signal sources with recently proposed correlated photonic-dimer sources. In the low-photon-rate regime, the dimer sources in both the Bose–Einstein condensate (BEC) and Bardeen–Cooper–Schrieffer (BCS) limits yield substantial capacity improvements over conventional sources. Specifically, at the operationally relevant PPM order of M = 128, the increase relative to lasers reaches up to ∼37% (BEC) and ∼94% (BCS), respectively. These results underscore photon-statistics and correlation engineering as a promising degree of freedom for maximizing photon information efficiency under stringent power and transceiver constraints.

DOI
10.1364/ol.592295

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This work investigates the enhancement of channel capacity in photon-starved deep-space optical links by leveraging inter-photon correlations. We analyze an M-ary pulse-position modulation (PPM) photon-counting channel in the presence of Poisson background noise and compare conventional signal sources with recently proposed correlated photonic-dimer sources. In the low-photon-rate regime, the dimer sources in both the Bose–Einstein condensate (BEC) and Bardeen–Cooper–Schrieffer (BCS) limits yield substantial capacity improvements over conventional sources. Specifically, at the operationally relevant PPM order of M = 128, the increase relative to lasers reaches up to ∼37% (BEC) and ∼94% (BCS), respectively. These results underscore photon-statistics and correlation engineering as a promising degree of freedom for maximizing photon information efficiency under stringent power and transceiver constraints.
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The information capacity of an optical channel under power constraints is ultimately limited by the quantum nature of transmitted signals. We discuss currently available and emerging photonic technologies whose combination can be shown theoretically to enable nearly quantum-limited operation of a noisy optical communication link in the photon-starved regime, with the information rate scaling linearly in the detected signal power. The key ingredients are quantum pulse gating to facilitate mode selectivity, photon-number-resolved direct detection, and a photon-efficient high-order modulation format such as pulse position modulation, frequency shift keying, or binary phase shift keyed Hadamard words decoded optically using structured receivers.
This paper presents a practical optical communication framework that transmits binary information using distinct coherent states characterized by different mean photon numbers and detects the received signals via threshold-based photon counting. Unlike conventional approaches that often assume idealized detection environments, we rigorously analyze the performance of the proposed scheme under three realistic scenarios: (i) noise-free channels, (ii) channels impaired by additive Poisson noise, and (iii) turbulent free-space optical channels with fading and background noise. The coherent-state modulation enables energy-efficient transmission in the quantum-limited regime while the photon-counting receiver employs a statistically optimized decision threshold to discriminate between received photon-count levels. To address the lack of instantaneous channel state information in fading environments, we further propose a pilot-based channel estimation method that enables adaptive threshold selection. Closed-form expressions for decision thresholds and error probabilities are derived, and the effectiveness of the scheme is validated through detailed numerical simulations. These results offer design insights for photon-efficient, low-power optical communication systems operating under realistic physical impairments.
We investigate modulation and coding techniques that approach the fundamental limits of communication and key distribution over optical channels, in the regime of simultaneously high photon and bandwidth efficiencies. First, we develop a simple and robust system design for free-space optical communication that incorporates pulse-position modulation (PPM) over multiple spatial degrees of freedom in order to achieve high photon and spectral efficiency. Further, in the context of key distribution, we determine the optimal rate using a Poisson source of entangled photon pairs and photon detectors, and show how to approach it using PPM parsing of the detected photon stream.
The binary (one-bit-per-photon) encoding that most existing quantum key distribution (QKD) protocols employ puts a fundamental limit on their achievable key rates, especially under high channel loss conditions associated with long-distance fiber-optic or satellite-to-ground links. Inspired by the pulse-position-modulation (PPM) approach to photon-starved classical communications, we design and demonstrate the first PPM-QKD, whose security against collective attacks is established through continuous-variable entanglement measurements that also enable a novel decoy-state protocol performed conveniently in post processing. We achieve a throughput of 8.0 Mbit/s (2.5 Mbit/s for loss equivalent to 25 km of fiber) and secret-key capacity up to 4.0 bits per detected photon, thus demonstrating the significant enhancement afforded by high-dimensional encoding. These results point to a new avenue for realizing high-throughput satellite-based or long-haul fiber-optic quantum communications beyond their photon-reception-rate limits.