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Entropy

Binary Communication with Gazeau–Klauder Coherent States

Jerzy Dajka, J. Łuczka

Published Feb 10, 2020• 6 citations
Publisher

Abstract

We investigate advantages and disadvantages of using Gazeau-Klauder coherent states for optical communication. In this short paper we show that using an alphabet consisting of coherent Gazeau-Klauder states related to a Kerr-type nonlinear oscillator instead of standard Perelomov coherent states results in lowering of the Helstrom bound for error probability in binary communication. We also discuss trace distance between Gazeau-Klauder coherent states and a standard coherent state as a quantifier of distinguishability of alphabets.

DOI
10.3390/e22020201

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We investigate advantages and disadvantages of using Gazeau-Klauder coherent states for optical communication. In this short paper we show that using an alphabet consisting of coherent Gazeau-Klauder states related to a Kerr-type nonlinear oscillator instead of standard Perelomov coherent states results in lowering of the Helstrom bound for error probability in binary communication. We also discuss trace distance between Gazeau-Klauder coherent states and a standard coherent state as a quantifier of distinguishability of alphabets.
In quantum information processing, using a receiver device to differentiate between two nonorthogonal states leads to a quantum error probability. The minimum possible error is known as the Helstrom bound. In this work, we study statistical aspects and quantum limits for states that generalize the Glauber–Sudarshan coherent states, such as nonlinear, Perelomov, Barut–Girardello, and (modified) Susskind–Glogower coherent states. For some of these, we show that the Helstrom bound can be significantly lowered and even vanish in specific regimes.
Part of the difficulties in implementing communication in quantum information stems from the fragility of Schrödinger's cat-like superpositions. A recent experiment in quantum optics by Cook et al (2007 Nature 446 774) has proved the feasibility of a feedback-mediated quantum measurement for discriminating between optical coherent states under photodetection. Minimizing the error in receiver measurement over all possible POVMs leads to the so-called quantum error probability or 'Helstrom bound', and CMG measurements validate the theoretical prediction by Helstrom, Dolinar and Geremia concerning this bound. In this work, we present some preliminary theoretical and numerical explorations concerning the properties of the Helstrom bound in binary (or multibinary) communication involving non-Poissonian or nonlinear coherent states.
In this work, we study the physical and mathematical characteristics of Barut–Giradello coherent states for the isotonic oscillator. Some relevant optical and statistical properties are analyzed and discussed. Furthermore, the thermodynamic and temporal stabilities are obtained, respectively, from [Formula: see text]-representation of the density operator, and probability density approaches. In addition, a comparative analysis of non-classical behaviors is made between these states and those of the Gazeau–Klauder type constructed for this quantum system.