Optimal unambiguous discrimination of quantum states

Jafarizadeh, M. A.; Rezaei, M.; Karimi, N.; Amiri, Abolfazl

doi:10.1103/physreva.77.042314

Cited by 52 publications

(76 citation statements)

References 24 publications

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“…The topic of quantum state discrimination was firmly established in the 1970s by the pioneering work of Helstrom [2], who considered a minimum error discrimination of two known quantum states and unambiguous state discrimination was originally formulated and analyzed by Ivanovic, Dieks, and Peres [3,4,5] in 1987. [6] In this paper, we deal with minimum-error discrimination discrimination. We will use convex optimization [7] as a tool for reaching this aim, which has many other different applications where some of them have been seen in previous papers [6,8,9,10,11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

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The minimum-error discrimination via Helstrom family of ensembles and convex optimization

Jafarizadeh

Mazhari

Aali

2010

Quantum Inf Process

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Using the convex optimization method and Helstrom family of ensembles introduced in Ref.[1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid.

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Section: Introductionmentioning

confidence: 99%

“…[6] In this paper, we deal with minimum-error discrimination discrimination. We will use convex optimization [7] as a tool for reaching this aim, which has many other different applications where some of them have been seen in previous papers [6,8,9,10,11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

The minimum-error discrimination via Helstrom family of ensembles and convex optimization

Jafarizadeh

Mazhari

Aali

2010

Quantum Inf Process

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“…USD is possible if and only if the initial states are linearly independent [9]. When N ≥ 3, some special cases were investigated in finding the optimal solutions [10][11][12][13]. Recently, USD was studied by means of a geometric view [14,15].…”

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Extracting remaining information from an inconclusive result in optimal unambiguous state discrimination

Zhang

et al. 2014

Quantum Inf Process

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In unambiguous state discrimination, the measurement results consist of the error-free results and an inconclusive result, and an inconclusive result is conventionally regarded as a useless remainder from which no information about initial states is extracted. In this paper, we investigate the problem of extracting remaining information from an inconclusive result, provided that the optimal total success probability is determined. We present three simple examples. An inconclusive answer in the first two examples can be extracted partial information, while an inconclusive answer in the third one cannot be. The initial states in the third example are defined as the highly symmetric states.

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“…Very recently, based on unambiguous discrimination, the topic of extracting information from a qubit by multiple observers has been studied [17,18]. Most of the existing results about optimal unambiguous discrimination were derived in the POVM formalism [12,19,20], which can be realized by introducing ancillary systems and performing von Neumann measurements on systems and the ancillas. The present work and previous studies [9][10][11]18] investigating unambiguous quantum state discrimination by using the language of system-ancilla provides a way to understand the roles of quantum correlations in the quantum information process.…”

Section: Lf Xu Et Almentioning

confidence: 99%

“…Since the solution of |η i for the absence of entanglement in state ρ SA is not unique, we choose the ones satisfying the equations (17)(18)(19)(20), which provides a uniform treatment to the four cases of priori probabilities and overlap. Since the GMQD is not normalized to one and its value for maximally entangled qutrit-qubit states is 0.5, we plot the quantity 2D G (ρ SA ) for the case with equal a priori overlaps in Fig.…”

Section: Lf Xu Et Almentioning

confidence: 99%

Assisted optimal state discrimination without entanglement

Zhang

Liang

et al. 2014

EPL

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PACS 03.65.Ta -Foundations of quantum mechanics; measurement theory PACS 03.67.Mn -Entanglement measures, witnesses, and other characterizations PACS 42.50.Dv -Quantum state engineering and measurements Abstract -A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of d states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a priori probabilities. By improving the protocol in [Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play as a key role in optimal state discrimination assisted by a qubit for more general cases.Introduction. -Quantum correlations contained in composite quantum states play important roles in quantum information processing and have been widely studied from various perspectives. Many concepts have been presented to reflect these correlations, such as quantum entanglement [1], Bell nonlocality [2], and quantum discord [3,4]. Entanglement had been regarded as the only resource for demonstrating the superiority of quantum information processing [1,5]. However, recent studies [6,7] show that the algorithm for deterministic quantum computation with one qubit (DQC1) can surpass the performance of the corresponding classical algorithm in the absence of entanglement between the control qubit and a completely mixed state. The quantum discord, which measures the nonclassical correlations and can exist in a separable state, is regarded to be the key resource in this quantum algorithm and has gained wide attention in recent years. Based on a unified view [8] of quantum and classical correlations, another type of quantum correlations called dissonance was put forward. Quantum dissonance measures the nonclassical correlations with entanglement being completely excluded. For a separable state, its dissonance is exactly

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Optimal unambiguous discrimination of quantum states

Cited by 52 publications

References 24 publications

The minimum-error discrimination via Helstrom family of ensembles and convex optimization

The minimum-error discrimination via Helstrom family of ensembles and convex optimization

Extracting remaining information from an inconclusive result in optimal unambiguous state discrimination

Assisted optimal state discrimination without entanglement

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