The description of Gaussian noise for single-mode quantum fields is briefly reviewed and applied to calculate the maximal information properties of three quantum communication channels degraded by Gaussian noise. These channels are based on (i) heterodyne detection of coherent states, (ii) homodyne detection of squeezed states, and (iii) photodetection of number states. It is found that each channel can outperform the others for a given noise level, where the optimum channel is essentially determined by the product of the average noise and signal energies.
The description of Gaussian noise for single-mode quantum fields is briefly reviewed and applied to calculate the maximal information properties of three quantum communication channels degraded by Gaussian noise. These channels are based on (i) heterodyne detection of coherent states, (ii) homodyne detection of squeezed states, and (iii) photodetection of number states. It is found that each channel can outperform the others for a given noise level, where the optimum channel is essentially determined by the product of the average noise and signal energies.
We address binary optical communication in single-mode and entangled quantum noisy channels. For single mode we present a systematic comparison between direct photodetection and homodyne detection in realistic conditions, i.e. taking into account the noise that occurs during both the propagation and the detection of the signals. We then consider entangled channels based on a twin-beam state of radiation, and show that with realistic heterodyne detection the error probability at fixed channel energy is reduced in comparison with the single-mode cases for a large range of values of quantum efficiency and noise parameters.
Communication theory applied to lightwave channels is ordinarily carried out using the semiclassical theory of photodetection. Recent development of nonclassical light sources-whose photodetection statistics require the use of quantum theory-plus increasing interest in optics-based approaches to quantum information processing necessitates a thorough understanding of the similarities and distinctions between the semiclassical and quantum theories of optical communications. This paper is addressed to that need, focusing, for convenience, on the free-space communication channel using Gaussian states of light. The quantum version of the Huygens-Fresnel diffraction integral is reviewed, along with the semiclassical and quantum theories of direct, homodyne, and heterodyne detection. Maximally entangled Gaussian state light is used, in conjunction with quantum photodetection theory, to explain the nonclassical effects seen in Hong-Ou-Mandel interferometry and violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality. The classical information capacities of several bosonic channels are reviewed, and shown to exceed what can be achieved using conventional optical receivers.
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated codewords with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations (passive linear optics: beamsplitters and phase-shifters, second order nonlinear process (squeezers), along with homodyne or heterodyne detection measurements) and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communications, one has to incorporate non-Gaussian (i.e. higher order nonlinear) operations in the receiver.
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated code words with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent-state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations [passive linear optics: beam splitters and phase shifters; second-order nonlinear optics (or active linear optics): squeezers, along with homodyne or heterodyne detection measurements] and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communication, one has to incorporate non-Gaussian, i.e., third- or higher-order nonlinear operations in the receiver. Finally we compare our Gaussian receiver limit with experimentally feasible non-Gaussian receivers and show that in the regime of low received photon flux, it is possible to overcome the Gaussian receiver limit by relatively simple non-Gaussian receivers based on photon counting.
The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number N and allowed average decoding error ε equals the vanishing-error capacity at mean photon number N/(1−ε). Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.
For a fixed mean signal energy, the optimal narrow-band bosonic channel is based on photodetection of a Bose-Einstein distribution of number states. A simple formula is obtained for the average error probability per symbol of this channel when degraded by Gaussian noise and inefficient detection. A general information bound is derived for narrow-band channels degraded by Gaussian noise, which yields a lower bound for the average probability of error per bit. Results are applicable to all number-state channels in the limit of low noise and high efficiency.