Optimal distinction between two non-orthogonal quantum states

Jaeger, Gregg; Shimony, Abner

doi:10.1016/0375-9601(94)00919-g

Cited by 315 publications

(308 citation statements)

References 3 publications

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“…The optimal POVM (28) can be also obtained numerically. We demonstrate feasibility of iterative solution of the symmetrized extremal equations (16), (17), (18), and (19) for mixed quantum states (26) with the angle of separation θ = π/4. The trade-off of the relative success rate and the probability of inconclusive results is shown in Fig.…”

Section: Discrimination Between Two Mixed Qubit Statesmentioning

confidence: 97%

“…An interesting alternative approach has been suggested by Ivanovic, Dieks, and Peres (IDP) for the discrimination of two pure states [14,15,16,17] and extended to N linearly independent states by Chefles and Barnett [18,19,20,21]. These states can be discriminated unambiguously, provided that we allow for some fraction of the inconclusive results P I .…”

Section: Introductionmentioning

confidence: 99%

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Optimal discrimination of mixed quantum states involving inconclusive results

2003

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We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.

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Section: Discrimination Between Two Mixed Qubit Statesmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Optimal discrimination of mixed quantum states involving inconclusive results

2003

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“…These authors found the optimal solution when the two states are being selected from an ensemble in which they are equally likely. The optimal solution for the situation in which the states have different weights was found by Jaeger and Shimony [4]. We proposed an optical implementation of the optimal procedure along with a more compact rederivation of the general results and also showed that the method is useful in other areas of quantum information processing [5] such as, for example, entanglement enhancement [6].…”

Section: Introductionmentioning

confidence: 94%

“…If we denote by Q ′′ the average probability of failure when distinguishing between the two states {|ψ 1 and |ψ 2 }, we know that Q ′′ = |O 12 | (Refs. [1]- [4]). For the case we are considering, |O 12 | = |O 13 | = s, and we see that Q < Q ′′ .…”

Section: Comparison To the Case When All States Are Discriminatedmentioning

confidence: 99%

Optimum unambiguous discrimination between subsets of nonorthogonal quantum states

2002

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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, {|ψ1 , |ψ2 , |ψ3 }, we show that the optimal strategy to distinguish |ψ1 from the set {|ψ2 , |ψ3 } 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) which provide an optical implementation of the optimal strategy.

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“…A more general bound for two states with arbitrary a priori probabilities was later obtained by Jaeger and Shimony [6].…”

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confidence: 94%

Experimental demonstration of optimal unambiguous state discrimination

et al. 2001

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We present the first full demonstration of unambiguous state discrimination between non-orthogonal quantum states. Using a novel free space interferometer we have realised the optimum quantum measurement scheme for two non-orthogonal states of light, known as the Ivanovic-Dieks-Peres (IDP) measurement. We have for the first time gained access to all three possible outcomes of this measurement. All aspects of this generalised measurement scheme, including its superiority over a standard von Neumann measurement, have been demonstrated within 1.5% of the IDP predictions.

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Optimal distinction between two non-orthogonal quantum states

Cited by 315 publications

References 3 publications

Optimal discrimination of mixed quantum states involving inconclusive results

Optimal discrimination of mixed quantum states involving inconclusive results

Optimum unambiguous discrimination between subsets of nonorthogonal quantum states

Experimental demonstration of optimal unambiguous state discrimination

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