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arXiv:2501.13356 · Physical Review Research

Communicating at a record 14.5 bits per received photon through a photon-starved channel

Sai Kanth Dacha, René-Jean Essiambre, Alexei Ashikhimin, Andrea Blanco‐Redondo, Frank R. Kschischang, Konrad Banaszek, Yuanhang Zhang

Published Jul 16, 2025• 2 citations
arXivHTMLPDF

Abstract

Exploration of the Universe requires communication with Earth, either on a direct path or through a cascade of proximate celestial bodies. Microwaves have traditionally been used for space communication, but electromagnetic waves of higher frequencies, such as in the optical domain, will enable probing farther in space due to their considerably lower diffraction loss. The ultimate range limit to point-to-point optical communication, at a given transmitter power, is determined by the photon information efficiency (PIE), which measures the number of information bits extracted per photon incident on a detector. As distances across space and, consequently, path loss increases, systems achieving the highest PIE can enable communication at the longest distances. We report here an experimental demonstration of optical detection at a record PIE of 14.5 bits per incident photon, or 17.8 bits per detected photon, after 87.5 dB of attenuation. Expressed in terms of energy per bit, this corresponds to 8.84 zeptojoules per bit, or 0.069 photons per bit at 1550 nm. To our knowledge, this is the highest PIE or lowest energy per bit detection system ever demonstrated at optical frequencies. Such a sensitive detection system holds promise for a wide range of applications.

DOI
10.1103/mmth-7tww

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Exploration of the Universe requires communication with Earth, either on a direct path or through a cascade of proximate celestial bodies. Microwaves have traditionally been used for space communication, but electromagnetic waves of higher frequencies, such as in the optical domain, will enable probing farther in space due to their considerably lower diffraction loss. The ultimate range limit to point-to-point optical communication, at a given transmitter power, is determined by the photon information efficiency (PIE), which measures the number of information bits extracted per photon incident on a detector. As distances across space and, consequently, path loss increases, systems achieving the highest PIE can enable communication at the longest distances. We report here an experimental demonstration of optical detection at a record PIE of 14.5 bits per incident photon, or 17.8 bits per detected photon, after 87.5 dB of attenuation. Expressed in terms of energy per bit, this corresponds to 8.84 zeptojoules per bit, or 0.069 photons per bit at 1550 nm. To our knowledge, this is the highest PIE or lowest energy per bit detection system ever demonstrated at optical frequencies. Such a sensitive detection system holds promise for a wide range of applications.
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.
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.
We address the problem of how efficiently information can be encoded into and read out reliably from a passive reflective surface that encodes classical data by modulating the amplitude and phase of incident light. We show that nature imposes no fundamental upper limit to the number of bits that can be read per expended probe photon and demonstrate the quantum-information-theoretic trade-offs between the photon efficiency (bits per photon) and the encoding efficiency (bits per pixel) of optical reading. We show that with a coherent-state (ideal laser) source, an on-off (amplitude-modulation) pixel encoding, and shot-noise-limited direct detection (an overly optimistic model for commercial CD and DVD drives), the highest photon efficiency achievable in principle is about 0.5 bits read per transmitted photon. We then show that a coherent-state probe can read unlimited bits per photon when the receiver is allowed to make joint (inseparable) measurements on the reflected light from a large block of phase-modulated memory pixels. Finally, we show an example of a spatially entangled nonclassical light probe and a receiver design---constructible using a single-photon source, beam splitters, and single-photon detectors---that can in principle read any number of error-free bits of information. The probe is a single photon prepared in a uniform coherent superposition of multiple orthogonal spatial modes, i.e., a WWW state. The code and joint-detection receiver complexity required by a coherent-state transmitter to achieve comparable photon efficiency performance is shown to be much higher in comparison to that required by the WWW-state transceiver, although this advantage rapidly disappears with increasing loss in the system.
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.
Optical communication with high photon-efficiency (many bits/photon) and high spectral efficiency (SE) (many bits/s-Hz) cannot be achieved unless multiple spatial modes are employed. For vacuum propagation, it is known that achieving 10 bits/photon and 5 bits/s-Hz requires 189 low-loss spatial modes at the ultimate Holevo limit and 4500 such modes at the Shannon limit for on-off keying with direct detection. For terrestrial propagation paths, however, atmospheric turbulence corrupts multiple spatial-mode operation. This paper derives power-transmissivity bounds and average intermodal crosstalks for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green's function. These statistics are then evaluated for ~ 200 spatial-mode systems whose transmitters use either focused-beam, Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes and whose receivers either do or do not employ adaptive optics. It is shown that: (1) adaptive optics are not necessary for achieving both high photon information efficiency (PIE) and high SE; (2) systems employing HG or LG modes achieve the same capacities through turbulence; and (3) the orbital angular momentum carried by LG modes does not provide turbulence immunity. In the companion paper [N. Chandrasekaran, J. H. Shapiro, and L. Wang, “Photon Information Efficient Communication Through Atmospheric Turbulence-Part II: Bounds on Ergodic Classical and Private Capacities,” J. Lightw. Technol., vol. 32, no. 6, pp. 1088-1097, Mar. 2014], the transmissivity bounds are used to quantify the turbulence-induced loss in PIE versus SE performance for these mode sets.