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IEEE International Symposium on Information Theory (ISIT)

Information Rate loss from radiation decoherence

Alfonso García Martínez

Published Jun 1, 2009• 0 citations
Publisher

Abstract

The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The classical coherent-state Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, the information rates in the presence of decoherence essentially coincide with those over a Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a significant loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.

DOI
10.1109/isit.2009.5205474

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IEEE Transactions on Information Theory•Oct 1, 1965•15 citations
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The classical coherent-state Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, the information rates in the presence of decoherence essentially coincide with those over a Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a significant loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, information rates over the photon gas model essentially coincide with those over the Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.
The information rates achievable with a photon-gas model of electromagnetic radiation are studied. At any frequency, information rates over the photon-gas model essentially coincide with the Shannon capacity when the signal-to-noise ratio is below a threshold. Only above the threshold does the photon gas incur in a significant loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40dB40\phantom{\rule{0.3em}{0ex}}\mathrm{dB}40dB for radio frequencies and vanishes at higher frequencies.
Recovering complex optical signals with high sensitivity is central to coherent communication and sensing. Beyond conventional homodyne and heterodyne reception, phase-conjugate twin-wave encoding and phase-sensitive joint detection offer an alternative strategy with enhanced sensitivity. Extending this approach to long-distance transmission of high-order-modulated signals is challenging because optical phase coherence must be maintained at the receiver. Here we experimentally demonstrate injection-locking-assisted phase-conjugated twin-wave reception of 200-MBaud signals with modulation formats up to 256-QAM over 100 km of optical fiber. Optical injection locking regenerates the local oscillator (LO) from a reference transmitted through the 16 dB-loss link, while pilot-assisted optical feedback stabilizes the relative signal-LO phase, enabling coherent combining of the phase-conjugated twin waves at a single balanced photodetector. At equal received signal-photon number per quadrature in each data-carrying optical mode, the measured PCTW signal-to-noise ratio (SNR) exceeds the ideal single-mode homodyne standard quantum limit (SQL) benchmark. The SNR gains over the measured homodyne and conventional heterodyne results are about 3 dB and 6 dB, respectively. Constellation and bit-error-rate measurements show that this gain improves high-order data recovery relative to heterodyne reception. An ideal Gaussian-noise model predicts a photon information efficiency of 1.54 bits per received signal photon for uniform 16-QAM. These results establish an injection-locking-assisted coherent receiver architecture that implements joint detection of phase-conjugated twin waves over 100 km of fiber with enhanced sensitivity, providing a practical route for photon-efficient coherent communication.
We consider a communication system consisting of an information source of electromagnetic radiation. It is assumed that the information source radiates an electromagnetic signal with an average power S, and the signal propagated through the electromagnetic channel is assumed to be perturbed by additive thermal noise at temperature T. For simplicity, we assume that the electromagnetic signal is one-dimensional (i.e., the photon fluctuation is restricted to only one polarized state), in which the propagation occurs in the same direction of the wave vectors. It is emphasized that the corresponding occupation number of the quantum levels can be fully described. Obviously, these occupation quantum levels correspond to the microsignal structure of the information source. It is therefore assumed that these occupation numbers can be uniquely determined for those representing an input signal ensemble. We further assume that an ideal receiver (an ideal photon counter) is used at the output end of the channel. That is, the receiver is able to detect the specified frequencies of the electromagnetic signal. It is also emphasized that in practice the interaction of the electromagnetic signal and the detector are strictly statistical, that is, a certain amount of information loss is expected at the output end of the receiver. The idealized model of the receiver we have proposed mainly simplifies the method by which the quantum effect on the communication channel can be easily calculated.
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.
In order to discover what effect the quantum nature of radiation has on the detection of signals at optical frequencies, the detectability of coherent and, in the threshold limit, incoherent signals is calculated on the basis of an idealized quantum-mechanical model of a receiver. The detectabilities reduce at low frequencies to those found by ordinary signal-detection theory; at high frequencies they depend on Planck's constant. For incoherent signals of high frequency the threshold detector is equivalent to a system that focuses the radiation on a photoelectric surface of unit quantum efficiency and optimally processes the emitted electrons.