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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Four-state discrimination via a homodyne-Kennedy hybrid receiver

Mario A. Usuga, Christian Muller, Christoffer Wittmann, Masahiro Takeoka, Ulrik L. Andersen, Gerd Leuchs

Published Jun 1, 2009• 1 citation
Publisher

Abstract

Quantum communication allows for deep space communication and secure transmission of information. The perfomance and security of such protocols is based on the non-orthogonality of the used states, which is a key feature of quantum mechanics. The task of a quantum receiver is to discriminate between different states in a given alphabet with minimum error. This gives rise to the necessity of having receivers with a minimum amount of discrimination errors approaching the limits imposed by quantum mechanics [1,2]. Conventional detection schemes fail to fulfill this task, which makes the study of quantum receivers an important field in the realm of quantum communication.

DOI
10.1109/cleoe-eqec.2009.5194771

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Quantum communication allows for deep space communication and secure transmission of information. The perfomance and security of such protocols is based on the non-orthogonality of the used states, which is a key feature of quantum mechanics. The task of a quantum receiver is to discriminate between different states in a given alphabet with minimum error. This gives rise to the necessity of having receivers with a minimum amount of discrimination errors approaching the limits imposed by quantum mechanics [1,2]. Conventional detection schemes fail to fulfill this task, which makes the study of quantum receivers an important field in the realm of quantum communication.
Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its minimum achievable error rate often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We design two discrimination protocols that surpass the Gaussian limit: one using non-Gaussian unitary operations with homodyne detection, and another based on orthogonal polynomials. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes.
Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states---the quantum states of light emitted by an ideal laser---has immense practical importance. Due to fundamental limits imposed by quantum mechanics, such discrimination has a finite minimum probability of error. While concrete optical circuits for the optimal discrimination between two coherent states are well known, the generalization to larger sets of coherent states has been challenging. In this paper, we show how to achieve optimal discrimination of any set of coherent states using a resource-efficient quantum computer. Our construction leverages a recent result on discriminating multicopy quantum hypotheses [Blume-Kohout, Croke, and Zwolak, arXiv:1201.6625]. As illustrative examples, we analyze the performance of discriminating a ternary alphabet and show how the quantum circuit of a receiver designed to discriminate a binary alphabet can be reused in discriminating multimode hypotheses. Finally, we show that our result can be used to achieve the quantum limit on the rate of classical information transmission on a lossy optical channel, which is known to exceed the Shannon rate of all conventional optical receivers.
Standard protocols in optical communication systems employ coherent states of light as the information carriers. The quantum nature inherent to these states introduces a fundamental complexity into the decoding process. In particular, when dealing with attenuated signals, the overlap between different states precludes the possibility of perfectly discriminate them. In this study, we investigate the performance of conventional and nonconventional quantum discrimination strategies under different informational metrics. We focus our analysis on binary coherent states within the ideal case of a lossless channel. The usual homodyne receiver was studied in comparison with the Kennedy and the optimized displacement receiver. We find that nonconventional strategies employing non-Gaussian measurements surpass the conventional homodyne discrimination scheme according to measurement error probability and mutual information.