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Journal of Physics Conference Series

Coherent states in Quantum Information: An example of experimental manipulations

Jean‐Pierre Gazeau

Published Mar 1, 2010• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/213/1/012013

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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.
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.
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.
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example, they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom bound, measurement of the phase of a quantum oscillator with accuracy approaching (or in some cases attaining) the Heisenberg limit (HL), and estimation of phase in interferometry with a variance scaling at the HL, using only single qubit measurement and control. Each of these examples has close links with quantum information, in particular, experimental optical quantum information: the first is a basic quantum communication protocol; the second has potential application in linear optical quantum computing; the third uses an adaptive protocol inspired by the quantum phase estimation algorithm. We discuss each of these examples and their implementation in the laboratory, but concentrate upon the last, which was published most recently [Higginset al.,Nature, vol. 450, p. 393, 2007].
Quantum optics has proved a fertile field for experimental tests of quantum information science, from experimental verification of the violation of the Bell inequalities to quantum teleportation. However it was long believed that quantum optics would not provide a practical path to efficient and scaleable quantum computation, and most current efforts to achieve a scaleable quantum computer have focussed on solid state implementations. This orthodoxy was challenged recently when Knill et al. showed that given single photon sources and single photon detectors, linear optics alone would suffice to implement efficient quantum computation. While this result is surprising, the complexity of the optical networks required is daunting. In this talk we propose an efficient scheme which is elegant in its simplicity. We indicate how fundamental single and two qubit gates can be achieved. By encoding the quantum information in multi-photon coherent states, rather than single photon states, simple optical manipulations acquire unexpected power. As an application of this new information processing ability we investigate a class of high precision measurements. We show how superpositions of coherent states allow displacement measurements at the Heisenberg limit. Entangling many superpositions of coherent states offers a significant advantage over a single mode superposition states with the same mean photon number.