Optimized maximum-confidence discrimination of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>mixed quantum states and application to symmetric states

Herzog, Ulrike

doi:10.1103/physreva.85.032312

Cited by 13 publications

(39 citation statements)

References 38 publications

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“…Then, we show that by implementing an optimized maximum-confidence (MC) measurement [19] to accomplish this task, she can perform the optimal imperfect conclusive teleportation as described above. The MC discrimination for the aforementioned set of states was studied recently [20,21]. Specifically, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Quantum teleportation via maximum-confidence quantum measurements

et al. 2012

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We investigate the problem of teleporting unknown qudit states via pure quantum channels with nonmaximal Schmidt rank. This process is mapped to the problem of discriminating among nonorthogonal symmetric states which are linearly dependent and equally likely. It is shown that by applying an optimized maximum-confidence (MC) measurement for accomplishing this task, one reaches the maximum possible teleportation fidelity after a conclusive event in the discrimination process, which in turn occurs with the maximum success probability. In this case, such fidelity depends only on the Schmidt rank of the channel and it is larger than the optimal one achieved, deterministically, by the standard teleportation protocol. Furthermore, we show that there are quantum channels for which it is possible to apply a k-stage sequential MC measurement in the discrimination process such that a conclusive event at any stage leads to a teleportation fidelity above the aforementioned optimal one and, consequently, increases the overall success probability of teleportation with a fidelity above this limit.Comment: 14 pages, 6 figure

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Section: Introductionmentioning

confidence: 99%

Quantum teleportation via maximum-confidence quantum measurements

et al. 2012

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“…One interesting scheme is the maximum-confidence measurement analyzed in Refs. [7][8][9]. In the other scheme, considered in Refs.…”

Section: Introductionmentioning

confidence: 99%

Discrimination with an error margin among three symmetric states of a qubit

2012

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We consider a state discrimination problem which deals with settings of minimum-error and unambiguous discrimination systematically by introducing a margin for the probability of an incorrect guess. We analyze discrimination of three symmetric pure states of a qubit. The measurements are classified into three types, and one of the three types is optimal depending on the value of the error margin. The problem is formulated as one of semidefinite programming. Starting with the dual problem derived from the primal one, we analytically obtain the optimal success probability and the optimal measurement that attains it in each domain of the error margin. Moreover, we analyze the case of three symmetric mixed states of a qubit.

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“…The second approach has recently been solved for the case of two pure states with arbitrary occurrence probabilities [12], but it is not obvious whether the method can be extended to other cases involving, e.g., mixed states, more than two states, etc. Furthermore the connection with the first approach remains unnoticed, and the connection with the MC scheme has only been briefly discussed previously [5,14].Here we state some fundamental features of the optimal discrimination with fixed rate of inconclusive outcome (FRIO) scheme, in particular of the function P min e (Q), and show its links to the other schemes discussed above. We thus give a complete unified picture of quantum state discrimination.…”

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Optimal discrimination of quantum states with a fixed rate of inconclusive outcomes

et al. 2012

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We present the solution to the problem of optimally discriminating among quantum states, i.e., identifying the states with maximum probability of success when a certain fixed rate of inconclusive answers is allowed. By varying the inconclusive rate, the scheme optimally interpolates between unambiguous and minimum error discrimination, the two standard approaches to quantum state discrimination. We introduce a very general method that enables us to obtain the solution in a wide range of cases and give a complete characterization of the minimum discrimination error as a function of the rate of inconclusive answers. A critical value of this rate is identified that coincides with the minimum failure probability in the cases where unambiguous discrimination is possible and provides a natural generalization of it when states cannot be unambiguously discriminated. The method is illustrated on two explicit examples: discrimination of two pure states with arbitrary prior probabilities and discrimination of trine states. State discrimination has long been recognized to play a central role in quantum information and quantum computing. In these fields the information is encoded in the state of quantum systems; thus, one often needs to identify in which of N known states {ρ i } N i=1 one such system was prepared. If the possible states are mutually orthogonal this is an easy task: we just set up detectors along these orthogonal directions and determine which one clicks (assuming perfect detectors). However, if the states are not mutually orthogonal the problem is highly nontrivial and optimization with respect to some reasonable criteria leads to complex strategies often involving generalized measurements. Finding such optimal strategies is the subject of state discrimination.The two fundamental state discrimination strategies are discrimination with minimum error (ME) and unambiguous discrimination (UD). In ME, every time a system is given and a measurement is performed on it a conclusion must be drawn about its state. Accordingly, the measurement is described by an N -element positive operator valued measure (POVM), where each element represents a conclusive outcome. Errors are permitted and in the optimal strategy the probability of making an error is minimized [1]. In UD, no errors are tolerated but at the expense of permitting an inconclusive measurement outcome, represented by the positive operator 0 . Hence, the corresponding POVM is = { i } N i=0 . When 0 clicks we do not learn anything about the state of the system and in the optimal strategy the probability of the inconclusive outcome is minimized [2]. It has been recognized that states can be discriminated unambiguously only if they are linearly independent [3]. Discrimination with maximum confidence (MC) can be applied to states that are not necessarily independent and for linearly independent states it reduces to unambiguous discrimination [4,5], so the MC scheme can be regarded as a generalized UD strategy.It is clear that UD (or MC for linearly dependent stat...

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Optimized maximum-confidence discrimination ofNmixed quantum states and application to symmetric states

Cited by 13 publications

References 38 publications

Quantum teleportation via maximum-confidence quantum measurements

Quantum teleportation via maximum-confidence quantum measurements

Discrimination with an error margin among three symmetric states of a qubit

Optimal discrimination of quantum states with a fixed rate of inconclusive outcomes

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