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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optimal detection device for unknown quantum channel

Miroslav Ježek

Published Nov 21, 2003• 0 citations
Publisher

Abstract

Discrimination task is treated in the case of only partial prior information from measurements of unknown quantum sources. The construction of the optimal discrimination device and estimation of quantum states produced by unknown sources is performed simultaneously. A communication through a noisy quantum channel is formulated in terms of the proposed discrimination protocol.

DOI
10.1117/12.545057

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Discrimination task is treated in the case of only partial prior information from measurements of unknown quantum sources. The construction of the optimal discrimination device and estimation of quantum states produced by unknown sources is performed simultaneously. A communication through a noisy quantum channel is formulated in terms of the proposed discrimination protocol.
We develop a state discrimination approach to unassisted quantum communication through a noisy quantum channel. Starting from the operational duality between entanglement recovery and state discrimination, we construct entanglement-generation codes with explicit decoders constructed from Petz recovery maps. The resulting error bounds hold for every number of channel uses and are expressed in terms of Petz-Rényi coherent information. For product sources, they yield exponential error decay at rates below coherent information.
Quantum state discrimination is a fundamental task in quantum information theory and also an important building block in practical quantum information applications. We here consider optimal state discrimination in a noisy environment in which quantum states may be corrupted due to the intervention of an environment. We show that even if there exists an unwanted interaction with an environment and the channel describing the interaction is not yet identified, a measurement prepared in the beginning for optimal state discrimination can be preserved as an optimal measurement ever after a channel use. This means that in a practical realization of quantum communication, verification of a channel can be circumvented and the cost of quantum tomography is saved. We also show a protocol of preserving an optimal measurement for state discrimination.
In this work, we consider optimal discrimination among quantum states that are sent through a quantum channel. We show the conditions on a quantum channel and an ensemble of states to preserve a measurement for optimal state discrimination over the channel. In particular, we show that for an ensemble of states where the states are given with equal a priori probabilities, an optimal measurement can be preserved over any quantum channel by applying local operations and classical communication, that is, by manipulating the quantum states before and after the channel application. Examples are provided for illustration in the case of quantum communication protocols. Our results can be readily applied to optimal state discrimination over various types of noise.
In quantum information and quantum computing, the carrier of information is some quantum system and information is encoded in its state. After processing the state in the quantum processor, the information has to be read out. Clearly, this task is equivalent to determining the final state of the system. We begin by briefly reviewing various possible state discrimination strategies that are optimal with respect to some reasonable criteria and report on recent advances in the unambiguous discrimination of mixed quantum states. This strategy has been successfully applied to devise a class of novel probabilistic quantum algorithms and has been demonstrated experimentally, using a linear optical implementation via generalized interferometers. In the second part we present a scheme for communication via completely unknown quantum states. In this context we discuss programmable quantum state discriminators that are universal, i.e. perform optimally on average, independently of the actual states used for the communication scheme. We conclude with a discussion of possible experimental implementations of the proposed device.
In quantum state discrimination, typically the design of measurement operators or probe state is formulated assuming the set of possible states is perfectly known, but this may yield designs which are sensitive to deviations in the realized set of states. For example, the channel through which a transmitted state is sent may not be deterministic, but instead characterized by a classical distribution over quantum channels. In this paper, we consider the design of measurement schemes and probe states for quantum detection over an uncertain quantum channel. We present stochastic gradient-based algorithms to maximize the expected performance over the channel distribution for various design objectives, including the detection probability and mutual information. Furthermore, we introduce a scheme that leverages the isometric extension of a quantum channel to measure the channel output in an enlarged Hilbert space such that the channels are more distinguishable, while simultaneously reducing the effective dimension and thereby reducing the optimization complexity. Finally, we apply the proposed algorithms to multicopy channel discrimination.