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Four-state discrimination scheme beyond the heterodyne limit

Christian R. Müller, Mario A. Usuga Castaneda, Christoffer Wittmann, Masahiro Takeoka, Christoph Marquardt, Ulrik L. Andersen, Gerd Leuchs

Published Jan 1, 2012• 0 citations
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Optics Express•Dec 9, 2025•2 citations
Discriminating coherent states of light is an important instance of quantum state discrimination that is central to all applications of laser light. We obtain the ultimate quantum limit on the error probability exponent for discriminating among any M multimode coherent-state signals via the recently developed theory of the quantum Chernoff exponent in M-ary multi-copy state discrimination. A receiver called the Sequential Waveform Nulling (SWN) receiver is proposed for discriminating an arbitrary coherent-state ensemble using only auxiliary coherent-state fields, beam splitters, and non-number-resolving single photon detectors. An explicit error probability analysis of the SWN receiver is used to show that it achieves the quantum limit on the error probability exponent, which is shown to be a factor of four greater than the error probability exponent of an ideal heterodyne-detection receiver on the same ensemble. Apart from being of fundamental interest, these results are relevant to communication, sensing, imaging, and quantum information processing systems that use laser light.
This paper proposes a hybrid receiver, the heterodyne-like feedforward partitioned-displacement hybrid (HFPH) receiver, for discriminating quadrature phase-shift keying (QPSK) coherent states using photon-number-resolving (PNR) detectors. The receiver integrates a heterodyne-like (HL) measurement scheme with a Shuro-like (SL) displacement backend, forming a feedforward architecture that dynamically adapts to real-time decisions. We theoretically analyze the performance of the proposed scheme under practical imperfections, including detection inefficiency, dark counts, and imperfect interference visibility. Our results demonstrate that the HFPH receiver can surpass the standard quantum limit under these non-ideal conditions and exhibits enhanced robustness compared to the benchmark receiver.