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arXiv:2112.02312 · Journal of the Optical Society of America B

Indirect measurement for optimal quantum communication enhanced by binary non-standard coherent states

Min Namkung, Jeong San Kim

Published Feb 28, 2022• 2 citations
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Abstract

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.

DOI
10.1364/josab.450647

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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.
It was known that a novel quantum communication protocol surpassing the shot noise limit can be proposed by an atomic indirect measurement based on the Jaynes-Cummings model. Moreover, the quantum communication with the atomic indirect measurement can nearly achieve the Helstrom bound as well as the accessible information when message is transmitted by an ideal coherent state. Here, we show that the atomic indirect measurement is robust against the phase-diffusion noise. By considering the error probability of discriminating received signal, we show that the atomic indirect measurement can also nearly achieve the Helstrom bound as well as the accessible information even the channel is exposed to the phase-diffused noise. Moreover, we further show that atomic indirect measurement outperforms the feedback-excluded receiver composed of a photon number resolving detector and maximum-a-posteriori decision rule when the standard deviation of the phase-diffusion channel is not too large.
Abstract A general scenario for an N -sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present article, we propose a new experimental scheme for the implementation of a sequential conclusive discrimination between binary coherent states via indirect measurements within the Jaynes–Cummings interaction model. We find that if the mean photon number is less than 1.6, then, for our two-sequential state discrimination scheme, the optimal success probability is larger than the one presented in Fields, Bergou, and Varga (2020, IEEE Int. Conf. Quant. Comp. Eng. ). We also show that, if the mean photon number is almost equal to 1.2, then the optimal success probability nearly approaches the Helstrom bound.
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.
We study the discrimination of weak coherent states of light with significant overlaps by nondestructive measurements on the light states through measuring atomic states that are entangled to the coherent states via dipole coupling. In this way, the problem of measuring and discriminating coherent light states is shifted to finding the appropriate atom–light interaction and atomic measurements. We show that this scheme allows us to attain a probability of error extremely close to the Helstrom bound, the ultimate quantum limit for discriminating binary quantum states, through the simple Jaynes–Cummings interaction between the field and ancilla with optimized light–atom coupling and projective measurements on the atomic states. Moreover, since the measurement is nondestructive on the light state, information that is not detected by one measurement can be extracted from the post-measurement light states through subsequent measurements.
We study the discrimination of weak coherent states of light with significant overlaps by nondestructive measurements on the light states through measuring atomic states that are entangled to the coherent states via dipole coupling. In this way, the problem of measuring and discriminating coherent light states is shifted to finding the appropriate atom–light interaction and atomic measurements. We show that this scheme allows us to attain a probability of error extremely close to the Helstrom bound, the ultimate quantum limit for discriminating binary quantum states, through the simple Jaynes–Cummings interaction between the field and ancilla with optimized light–atom coupling and projective measurements on the atomic states. Moreover, since the measurement is nondestructive on the light state, information that is not detected by one measurement can be extracted from the post-measurement light states through subsequent measurements.
We discuss an implementation of the minimum error state discrimination measurement, originally introduced by Helstrom [Quantum Detection and Estimation Theory (Academic Press, New York, 1976)]. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first entangled to an ancillary system and the measurement is performed on the ancilla. We show that, by an appropriate choice of the entanglement transformation, the Helstrom bound can be attained. The advantage of this approach is twofold. First, it provides an implementation when the optimal projective measurement cannot be directly performed. For example, in the case of continuous variable states (binary and NNN phase-shifted coherent signals), the available detection methods, photon counting and homodyning, are insufficient to perform the required cat-state projection. In the case of symmetric states, the square-root measurement is optimal, but it is not easy to perform directly for more than two states. Our approach provides a feasible alternative in both cases. Second, the measurement is nondestructive from the point of view of the original system and one has a certain amount of freedom in designing the post-measurement state, which can then be processed further.