arXiv subjects

Janos A. Bergou

Publications and source records attributed to Janos A. Bergou.

28 records · Page 2Linked to original sources

arXiv2005

Optimum measurement for unambiguously discriminating two mixed states: General considerations and special cases

Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A 71, 050301(R) (2005)] we investigate the optimum measurement for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. Unambiguous discrimination of nonorthogonal states is possible in a probabilistic way, at the expense of a nonzero probability of inconclusive results, where the measurement fails. Along with a discussion of the general problem, we give an example illustrating our method of solution. We also provide general inequalities for the minimum achievable failure probability and discuss in more detail the necessary conditions that must be fulfilled when its absolute lower bound, proportional to the fidelity of the states, can be reached.

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arXiv2005

An absolutely secure QKD scheme with no detection noise, entanglement and classical communication

A new quantum communication scheme is introduced which is the quantum realization of the classical Kish-Sethuraman (KS) cipher. First the message is bounced back with additional encryption by the Receiver and the original encryption is removed and the message is resent by the Sender. The mechanical analogy of this operation is using two padlocks; one by the Sender and one by the Receiver. We show that the rotation of the polarization is an operator which satisfies the conditions required for the KS encryption operators provided single photons are communicated. The new method is not only simple but has several advantages. The Evasdropper extracts zero information even if she executes a quantum measurement on the state. The communication can be done by two publicly agreed orthogonal states. Therefore, there is no inherent detection noise. No classical channel and no entangled states are required for the communication.

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arXiv2005

Optimum unambiguous discrimination of two mixed quantum states

We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we derive the conditions under which the failure probability of the measurement can reach its absolute lower bound, proportional to the fidelity of the states. The optimum measurement strategy yielding the fidelity bound of the failure probability is explicitly determined for a number of cases. One example involves two density operators of rank d that jointly span a 2d-dimensional Hilbert space and are related in a special way. We also present an application of the results to the problem of unambiguous quantum state comparison, generalizing the optimum strategy for arbitrary prior probabilities of the states.

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arXiv2005

Quantum-state filtering applied to the discrimination of Boolean functions

Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum state filtering. We derived previously the optimal strategy for the case of N non-orthogonal states, {|ψ_{1} >, ..., |ψ_{N} >}, for distinguishing |ψ_1 > from the set {|ψ_2 >, ..., |ψ_N >} and the corresponding optimal success and failure probabilities. In a previous paper [PRL 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill in the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased functions. The algorithm is probabilistic, it fails sometimes but when it does it lets us know that it did. Our approach can be considered as a generalization of the Deutsch-Jozsa algorithm that was developed for the discrimination of balanced and constant Boolean functions.

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arXiv2004

Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination

We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i. e. error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum error probability achievable in conclusive discrimination, and the minimum failure probability that can be reached in unambiguous discrimination of the same two states. The latter turns out to be at least twice as large as the former for any two given states. As an example, we treat the case that the state of the quantum system is known to be, with arbitrary prior probability, either a given pure state, or a uniform statistical mixture of any number of mutually orthogonal states. For this case we derive an analytical result for the minimum probability of error and perform a quantitative comparison to the minimum failure probability.

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arXiv2003

Quantum state filtering and discrimination between sets of Boolean functions

The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the filtering procedure is required to be unambiguous, which necessitates admitting inconclusive answers when the given states are not orthogonal. As an application, we propose an efficient, probabilistic procedure for distinguishing between sets of Boolean functions, which is an extension of the Deutsch-Jozsa algorithm.

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arXiv2003

Quantitative complementarity relations in bipartite systems

We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum properties predictability and visibility, for the most general quantum state of two qubits. Consequently, from an interferometric point of view, the usual wave-particle duality relation must be extended to a ``triality'' relation containing, in addition, the quantitative entanglement measure concurrence, which has no classical counterpart and manifests a genuine quantum aspect of bipartite systems. A generalized duality relation, that also governs possible violations of the Bell's inequality, arises between single- and bipartite properties.

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arXiv2002

Optimal unambiguous discrimination between subsets of non-orthogonal quantum states

It is known that unambiguous discrimination among non-orthogonal but linearly independent quantum states is possible with a certain probability of success. Here, we consider a variant of that problem. Instead of discriminating among all of the different states, we shall only discriminate between two subsets of them. In particular, for the case of three non-orthogonal states, we show that the optimal strategy to distinguish between a set containing one of the states from the set containing the other two has a higher success rate than if we wish to discriminate among all three states. Somewhat surprisingly, for unambiguous discrimination the subsets need not be linearly independent. A fully analytical solution is presented, and we also show how to construct generalized interferometers (multiports) that provide an optical implementation of the optimal strategy.

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arXiv2002

Minimum-error discrimination between subsets of linearly dependent quantum states

A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal quantum states occurring with given a priori probabilities. A general analytical solution is obtained for N states that are restricted to a two-dimensional subspace of the Hilbert space of the system. The result for the special case of three arbitrary but linearly dependent states is applied to a variety of sets of three states that are symmetric and equally probable. It is found that, in this case, the minimum error probability for distinguishing one of the states from the other two is only about half as large as the minimum error probability for distinguishing all three states individually.

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arXiv2002

Degree of entanglement in a quantum measurement process

We suggest a quantum measurement model in an ion trap which specifies the probability distribution of two, distinct internal ground states of a trapped four-level ion. The external degrees of motion of the four-level ion constitute the meter which, in turn, is coupled to the environment by engineered reservoirs. In a previous publication, a similar measurement model was employed to test decoherence effects on quantum nonlocality in phase space on the basis of coincidence measurements of the entangled system-meter scheme. Here, we study the effects of decoherence on the entanglement of formation characterized by the concurrence. The concurrence of the system enables to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question to what extend the Bell inequality can be considered as a measure of entanglement.

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