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arXiv:1304.7316 · IEEE Photonics Technology Letters

Suppressing the Errors Due to Mode Mismatch for $M$-Ary PSK Quantum Receivers Using Photon-Number-Resolving Detector

Ke Li, Yuan Zuo, Bing Zhu

Published Sep 16, 2013• 28 citations
arXivHTMLPDF

Abstract

An M-ary phase shift keying quantum receiver with photon-number-resolving detectors considering the mode mismatch between the signal and local oscillating fields is analyzed. Compared with the quantum receiver using ON-OFF detectors, the errors due to mode mismatch can be suppressed effectively using photon-number-resolving detectors, especially for larger signal mean photon numbers.

DOI
10.1109/lpt.2013.2282155

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Suppressing the Errors Due to Mode Mismatch for MMM-Ary PSK Quantum Receivers Using Photon-Number-Resolving Detector
An M-ary phase shift keying quantum receiver with photon-number-resolving detectors considering the mode mismatch between the signal and local oscillating fields is analyzed. Compared with the quantum receiver using ON-OFF detectors, the errors due to mode mismatch can be suppressed effectively using photon-number-resolving detectors, especially for larger signal mean photon numbers.
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A new strategy of iterative quantum receivers with photon-number-resolving detectors is proposed to discriminate coherent states. The iterative quantum receiver provides a bit error rate closer to the Helstrom limit when compared with a recently proposed non-iterative quantum receiver. Moreover, the proposed iterative receiver is robust against various imperfections, such as mode mismatch, non-ideal quantum efficiency and dark counts. The simulation results indicate that the iterative receiver is capable of achieving 2.16 dB improvement upon the standard quantum limit, leaving only 0.65 dB from the Helstrom limit. Besides, with Turbo encoder and decoder, the iterative receiver gives about 1.46 dB improvement over the conventional non-iterative quantum receiver and approaches the equivalent Helstrom limit.
We develop a theory of quantum M-ary phase shift keying in which quantum states of optical modes are modulated at the transmitter by applying one of M uniformly-spaced phase shifts. We allow full freedom in choosing modulation states with any number of signal, i.e., transmitted, and ancilla modes, subject only to an average energy, i.e., photon number, constraint in either the signal modes alone or in the signal and ancilla modes together. For lossless operation and unrestricted POVM measurements at the receiver, we find the explicit form of the modulation state that minimizes the average error probability under an energy constraint of N photons. Multiple signal modes, mixed states, and entanglement with an ancilla are shown to be unnecessary for optimum performance. We show that communication with zero error is possible if and only if N ≥ (M - 1)/2.
A quantum receiver is modelled as a harmonic oscillator imperfectly matched to the incident signal-bearing field. At the beginning of its interaction with the field the oscillator is primed by being placed in a predetermined quantum state. It is shown how to calculate the state of this oscillator at the end of the observation interval both in the presence and in the absence of an incident coherent signal. As examples the error probabilities of a binary on-off communication system with such a mismatched receiver are calculated (a) for a signal of known phase, the receiver primed with a two-photon coherent state, and (b) for a signal of random phase, the receiver primed with a number eigenstate. In both cases the error probability depends on the mean number of externally available signal photons when the number of photons in the priming state is very large, rather than on the smaller number that would actually be absorbed by the mismatched receiver unprimed.