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Frontiers in Optics

Quantum-Limited Discrimination between Laser Light and Noise

Jonathan L. Habif, Saikat Guha

Published Jan 1, 2018• 2 citations
Publisher

Abstract

We evaluate quantum limits and structured receiver performance for discriminating between a mode excited in a thermal versus a coherent state, and show an interesting inversion in receiver performance going from single-shot to collective measurements.
DOI
10.1364/ls.2018.lm1b.2

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Understanding the fundamental sensitivity limit of an optical sensor requires a full quantum mechanical description of the sensing task. In this work, we calculate the fundamental (quantum) limit for discriminating between pure laser light and thermal noise in a photon-starved regime. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. A generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We present an experimental demonstration of this sensing task and demonstrate a 15.4 dB improvement in discrimination sensitivity over direct detection using a GK receiver and an improvement of 19.4% in error probability over coherent detection.
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multicopy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is suboptimal in this multicopy case. Furthermore, for a large class of multicopy discrimination tasks between a pure and a mixed state, we prove that any Helstrom-bound achieving single-copy receiver is suboptimal by a factor of at least 2 in error-probability exponent compared to the multicopy quantum Chernoff bound. This behavior has a classical analog in the performance gap between soft-decision and hard-decision receivers for detecting a multicopy signal embedded in white Gaussian noise.
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.