This tutorial reviews the Holevo capacity limit as a universal tool to analyze the ultimate transmission rates in a variety of optical communication scenarios, ranging from conventional optically amplified fiber links to free-space communication with power-limited optical signals. The canonical additive white Gaussian noise model is used to describe the propagation of the optical signal. The Holevo limit exceeds substantially the standard Shannon limit when the power spectral density of noise acquired in the course of propagation is small compared to the energy of a single photon at the carrier frequency per unit time-bandwidth area. General results are illustrated with a discussion of efficient communication strategies in the photon-starved regime.

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Quantum Limits in Optical Communications

We propose a simple architecture based on multimode quantum memories for collective readout of classical information keyed using a pair coherent states, exemplified by the well-known binary phase shift keying format. Such a configuration enables demonstration of the superadditivity effect in classical communication over quantum channels, where the transmission rate becomes enhanced through joint detection applied to multiple channel uses. The proposed scheme relies on the recently introduced idea to prepare Hadamard sequences of input symbols that are mapped by a linear optical transformation onto the pulse position modulation format [Guha, S. Phys. Rev. Lett. 2011, 106, 240502]. We analyze two versions of readout based on direct detection and an optional Dolinar receiver which implements the minimum-error measurement for individual detection of a binary coherent state alphabet.

https://tandfonline.com/doi/pdf/10.1080/09500340.2016.1173731

Quantum memory receiver for superadditive communication using binary coherent states.

We discuss conceptual designs for structured optical receivers that can alleviate the requirement for high peak-to-average power ratio in photon-starved optical communication. The basic idea is to transmit sequences of suitably modulated coherent light pulses whose energy can be concentrated in a single temporal bin on the receiver side through optical interference. Two examples of scalable architectures for structured receivers are presented. The first one, based on active polarization switching, maps Hadamard codewords composed from the binary phase shift keying (BPSK) constellation onto the standard pulse position modulation (PPM) format. The second receiver, using solely passive optical elements, converts phase-polarization patterns of coherent light pulses into a single pulse preserving a synchronized time of arrival. Such a conversion enables implementation of a communication protocol equivalent to the PPM scheme but with distributed optical power provided that the intersymbol guard-time exceeds the pattern length.

Structured optical receivers for efficient deep-space communication

We analyze the information efficiency of a deep-space optical communication link with background noise, employing the pulse position modulation (PPM) format and a direct-detection receiver based on Geiger-mode photon counting The efficiency, quantified using Shannon mutual information, is optimized with respect to the PPM order under the constraint of a given average signal power in simple and complete decoding scenarios We show that the use of complete decoding, which retrieves information from all combinations of detector photocounts occurring within one PPM frame, allows one to achieve information efficiency scaling as the inverse of the square of the distance, ie proportional to the received signal power This represents a qualitative enhancement compared to simple decoding, which treats multiple photocounts within a single PPM frame as erasures and leads to inverse-quartic scaling with the distance We provide easily computable formulas for the link performance in the limit of diminishing signal power

Range dependence of an optical pulse position modulation link in the presence of background noise.

We analyze the performance of on-off keying (OOK) and its restricted version pulse position modulation (PPM) over a lossy narrowband optical channel under the constraint of a low average photon number, when direct detection is used at the output. An analytical approximation for the maximum PPM transmission rate is derived, quantifying the effects of photon statistics on the communication efficiency in terms of the g(2) second-order intensity correlation function of the light source. Enhancement attainable through the use of sub-Poissonian light is discussed.

Incoherent on-off keying with classical and non-classical light

We analyze the performance of on-off keying (OOK) and its restricted version pulse position modulation (PPM) over a lossy narrowband optical channel under the constraint of a low average photon number, when direct detection is used at the output. An analytical approximation for the maximum PPM transmission rate is derived, quantifying the effects of photon statistics on the communication efficiency in terms of the $g^{(2)}$ second-order intensity correlation function of the light source. Enhancement attainable through the use of sub-Poissonian light is discussed.

Piotr Kuszaj

Papers

Incoherent on-off keying with classical and non-classical light

Incoherent on-off keying with classical and non-classical light