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

Programmable state discriminators for the optimum discrimination of unknown quantum states (Invited Paper)

János A. Bergou

Published May 23, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.609940

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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 information and quantum computing, the carrier of information is some quantum system and information is encoded in its state. The state, however, is not an observable in quantum mechanics, thus a fundamental problem arises: after processing the information it has to be read out or, in other words, the state of the system must be determined. When the possible target states are orthogonal, this is a relatively simple task, provided the set of possible target states is known. But when the possible target states are not orthogonal their discrimination is far from being trivial even if their set is known. Thus the problem of discriminating among non-orthogonal states is ubiquitous in quantum information and quantum computing, underlying all communication and computing schemes. It is the subject of this talk to review recent theoretical and experimental advances in this field.
We discuss the problem of designing unambiguous programmable discriminators for any nnn unknown quantum states in an mmm-dimensional Hilbert space. The discriminator is a fixed measurement which has two kinds of input registers: the program registers and the data register. The program registers consist of the nnn states, while the data register is prepared among them. The task of the discriminator is to tell us which state stored in the program registers is equivalent to that in the data register. First, we give a necessary and sufficient condition for judging an unambiguous programmable discriminator. Then, if m=nm=nm=n, we present an optimal unambiguous programmable discriminator for them, in the sense of maximizing the worst-case probability of success. Finally, we propose a universal unambiguous programmable discriminator for arbitrary nnn quantum states. We also show how to use this universal discriminator to unambiguously discriminate mixed states.
In quantum information and quantum computing, the carrier of information is a quantum system and information is encoded in its state. Secure communication schemes employ non‐orthogonal states that can not be discriminated with 100% probability of success. We briefly review various possible optimized state discrimination strategies since they provide a quantitative figure of merit for the acceptable noise level in quantum communication. We also report on recent results in two special areas. First, we consider discrimination between mixed quantum states. Second, we show that communication via completely unknown quantum states is possible and discuss programmable quantum state discriminators that accomplish this task optimally.
We discuss the problem of designing unambiguous programmable discriminators for any nnn unknown quantum states in an mmm-dimensional Hilbert space. The discriminator is a fixed measurement that has two kinds of input registers: the program registers and the data register. The quantum state in the data register is what users want to identify, which is confirmed to be among the nnn states in program registers. The task of the discriminator is to tell the users which state stored in the program registers is equivalent to that in the data register. First, we give a necessary and sufficient condition for judging an unambiguous programmable discriminator. Then, if m=nm=nm=n, we present an optimal unambiguous programmable discriminator for them, in the sense of maximizing the worst-case probability of success. Finally, we propose a universal unambiguous programmable discriminator for arbitrary nnn quantum states.
We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers, and a third system, which is guaranteed to be prepared in one of the states stored in the program registers, is fed into the data register of the device. The device will then, with some probability of success, tell us whether the unknown state in the data register matches the state stored in the first or the second program register. We show that the optimal device, i.e., the one that maximizes the probability of success, is universal. It does not depend on the actual unknown states that we wish to discriminate.
Since the state of a quantum system is not an observable, it cannot be determined completely, in principle, if no a priori information is available. In this case, one needs to resort to various estimation strategies. The situation is completely different if a priori knowledge is available. Even unambigous discrimination is possible if the system is always prepared in a state that is selected from a known set of quantum states that are not orthogonal but linearly independent. This type of discrimination strategy has a higher probability of success by using generalised measurements than by using standard von Neumann measurements. We discuss here possible optical realizations, via generalized interferometers and single photon states, for the implementation of strategies that maximize the success rate. The implementations are based on exact analytical results. We also discuss possible applications for entanglement enhancement and quantum communication protocols.