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arXiv:2503.13161 · Optical Engineering

Photon information efficiency limits in deep-space optical communications

Marcin Jarzyna, Ludwig Kunz, Wojciech Zwoliński, Michał Jachura, Konrad Banaszek

Published Jan 11, 2024• 16 citations
arXivHTMLPDF

Abstract

Deep-space optical communication links operate under severely limited signal power, approaching the photon-starved regime that requires a receiver capable of measuring individual incoming photons. This makes the photon information efficiency (PIE), i.e., the number of bits that can be retrieved from a single received photon, a relevant figure of merit to characterize data rates achievable in deep-space scenarios. We review theoretical PIE limits assuming a scalable modulation format, such as pulse position modulation (PPM), combined with a photon counting direct detection receiver. For unrestricted signal bandwidth, the attainable PIE is effectively limited by the background noise acquired by the propagating optical signal. The actual PIE limit depends on the effectiveness of the noise rejection mechanism implemented at the receiver, which can be improved by the nonlinear optical technique of quantum pulse gating. Further enhancement is possible by resorting to photon number resolved detection, which improves discrimination of PPM pulses against weak background noise. The results are compared with the ultimate quantum mechanical PIE limit implied by the Gordon–Holevo capacity bound, which takes into account general modulation formats as well as any physically permitted measurement techniques.

DOI
10.1117/1.oe.63.4.041209

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Deep-space optical communication links operate under severely limited signal power, approaching the photon-starved regime that requires a receiver capable of measuring individual incoming photons. This makes the photon information efficiency (PIE), i.e., the number of bits that can be retrieved from a single received photon, a relevant figure of merit to characterize data rates achievable in deep-space scenarios. We review theoretical PIE limits assuming a scalable modulation format, such as pulse position modulation (PPM), combined with a photon counting direct detection receiver. For unrestricted signal bandwidth, the attainable PIE is effectively limited by the background noise acquired by the propagating optical signal. The actual PIE limit depends on the effectiveness of the noise rejection mechanism implemented at the receiver, which can be improved by the nonlinear optical technique of quantum pulse gating. Further enhancement is possible by resorting to photon number resolved detection, which improves discrimination of PPM pulses against weak background noise. The results are compared with the ultimate quantum mechanical PIE limit implied by the Gordon–Holevo capacity bound, which takes into account general modulation formats as well as any physically permitted measurement techniques.
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.
The ability to transmit information from one point to another using as low received power as possible has a fundamental impact in many contexts, including covert communication, energy-efficient networks, and communication over channels with extreme loss. An immediate application is deep-space exploration, in which there has been significant interest in moving from microwaves to optical signals due to considerably lower diffraction loss and larger bandwidth. At a given data rate and transmit power, systems with the highest photon information efficiency (PIE), defined as the number of information bits extracted per received photon, can bridge the largest loss. We report here an experimental demonstration, using large-order pulse-position modulation and superconducting single-photon detectors, of a record PIE of 14.5 (17.8) bits per incident (detected) photon after 87.5dB of channel loss. This corresponds to 8.84 zeptojoules, or 0.069 photons, per bit at 1550nm. The record result was achieved using a new low-complexity transmitter design that produces short optical pulses on-demand with an average extinction ratio exceeding 90dB per time slot. To our knowledge, this is the most sensitive optical detection system ever demonstrated for high-path-loss optical communication.
It is well known that ideal free-space optical communication at the quantum limit can have unbounded photon information efficiency (PIE), measured in bits per photon. High PIE comes at a price of low dimensional information efficiency (DIE), measured in bits per spatio-temporal-polarization mode. If only temporal modes are used, then DIE translates directly to bandwidth efficiency. In this paper, the DIE vs. PIE tradeoffs for known modulations and receiver structures are compared to the ultimate quantum limit, and analytic approximations are found in the limit of high PIE. This analysis shows that known structures fall short of the maximum attainable DIE by a factor that increases linearly with PIE for high PIE. The capacity of the Dolinar receiver is derived for binary coherent-state modulations and computed for the case of on off keying (OOK). The DIE vs. PIE tradeoff for this case is improved only slightly compared to OOK with photon counting. An adaptive rule is derived for an additive local oscillator that maximizes the mutual information between a receiver and a transmitter that selects from a set of coherent states. For binary phase-shift keying (BPSK), this is shown to be equivalent to the operation of the Dolinar receiver. The Dolinar receiver is extended to make adaptive measurements on a coded sequence of coherent state symbols. Information from previous measurements is used to adjust the a priori probabilities of the next symbols. The adaptive Dolinar receiver does not improve the DIE vs. PIE tradeoff compared to independent transmission and Dolinar reception of each symbol.
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.
An ideal intensity-modulated photon-counting channel can achieve unbounded photon information efficiencies (PIEs). However, a number of limitations of a physical system limit the practically achievable PIE. In this paper, we discuss several of these limitations and illustrate their impact on the channel. We show that, for the Poisson channel, noise does not strictly bound PIE, although there is an effective limit, as the dimensional information efficiency goes as e[overline] e PIE beyond a threshold PIE. Since the Holevo limit is bounded in the presence of noise, this illustrates that the Poisson approximation is invalid at large PIE for any number of noise modes. We show that a finite transmitter extinction ratio bounds the achievable PIE to a maximum that is logarithmic in the extinction ratio. We show how detector jitter limits the ability to mitigate noise in the PPM signaling framework. We illustrate a method to model detector blocking when the number of detectors is large, and illustrate mitigation of blocking with spatial spreading and altering. Finally, we illustrate the design of a high photon efficiency system using state-of-the-art photo-detectors and taking all these effects into account.