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Physica Scripta

Nonlinear coherent states for optimizing quantum information

Evaldo M. F. Curado, Jean‐Pierre Gazeau, Ligia M. C. S. Rodrigues

Published Aug 18, 2010• 8 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/82/03/038108

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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.
A part of difficulties in implementing communication in Quantum Information stems from the fragility of Shroedinger cat-like superpositions. We describe here a recent experiment in Quantum Optics proving the feasibility of a feedback-mediated quantum measurement for discriminating between optical coherent states under photodetection. The measurements validate theoretical prediction by Helstrom ("Helstrom bound"), Dolinar and Geremia. This contribution gives an account of the implementation achieved by Cook, Martin and Geremia (2007) and explains the theoretical approaches to the subject.
Quantum state discrimination between optical coherent superposition states is considered. The Helstrom bound for imperfect detection is evaluated. Under a physically realistic model of photodetection, we study several techniques for discriminating between optical coherent superposition states. We investigate quantum error probabilities for the Kennedy receiver, the Dolinar receiver and the unitary rotation scheme proposed by Sasaki and Hirota for sub-unity detector efficiency. Also, we study the feedback strategy employed by the Dolinar receiver to achieve the Helstrom bound for sub-unity detection efficiency.
It is well known that the Helstrom bound can be improved by generalizing the form of a coherent state. Thus, designing a quantum measurement achieving the improved Helstrom bound is important for novel quantum communication. In this paper, we analytically show that the improved Helstrom bound can be achieved by a projective measurement composed of orthogonal non-standard Schrödinger cat states. Moreover, we numerically show that the improved Helstrom bound can be nearly achieved by an indirect measurement based on the Jaynes–Cummings model. As the Jaynes–Cummings model describes an interaction between a light and a two-level atom, we emphasize that the indirect measurement considered in this paper has potential to be experimentally implemented.
One of the most crucial challenges in quantum communication is the discrimination of the non-orthogonal coherent states approaching the Helstrom limit. In this paper, a soft iterative quantum receiver is derived for discriminating among the coherent states. The receivers employing the iterative strategy for optimizing the feedback measurement are capable of operating closer to the theoretical error probability limit, actuating about 1.05 dB improvement over a recent proposed quantum receiver. The iterative quantum receivers achieve excellent performance despite using a reduced number of feedback measurement steps. Monte Carlo simulations are performed for quantifying the influence of practical quantum-domain impairments. These results suggest that iterative detection offers substantial robustness against many imperfections degrading realistic experimental implementation.
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.