Analysis of optimal unambiguous discrimination of three pure quantum states

Ha, Donghoon; Kwon, Younghun

doi:10.1103/physreva.91.062312

Cited by 21 publications

(19 citation statements)

References 22 publications

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“…In Conjecture 1, convex set C contains a line segment α i = 0, since there exists a case where Bob discriminates unambiguously remaining quantum states except i -th pure state. For N = 3, the geometric argument can be found in refs 31 – 33 . Let us assume that Bob’s set of post-measurement states, which corresponds to conclusive result of Bob, is .…”

Section: Resultsmentioning

confidence: 99%

“…Suppose that Alice prepares a quantum state out of two(or three) pure quantum states 6 – 9 , 31 – 33 .…”

Section: Resultsmentioning

confidence: 99%

“…Let the sub-matrices of be . When , is positive-semidefinite 32 , 33 . This condition indicates that three dimensional real vector ( α 1 , α 2 , α 3 ) ∈ C corresponding to Bob’s POVM satisfies the following relationship: Here, and Φ = ϕ 1 + ϕ 2 + ϕ 3 are refered to as a geometric phase 32 .…”

Section: Resultsmentioning

confidence: 99%

“…In this report, we study the structure of the convex set of linearly independent N pure states for sequential state discrimination, mainly dealing with the convex set of N = 3 31 – 33 . Because Bob performs an nonoptimal unambiguous discrimination, the real vector corresponding to Bob’s POVM exists inside the convex set.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Optimal Sequential State Discrimination for Linearly Independent Pure Quantum States

Namkung

Kwon

2018

Sci Rep

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Recently, J. A. Bergou et al. proposed sequential state discrimination as a new quantum state discrimination scheme. In the scheme, by the successful sequential discrimination of a qubit state, receivers Bob and Charlie can share the information of the qubit prepared by a sender Alice. A merit of the scheme is that a quantum channel is established between Bob and Charlie, but a classical communication is not allowed. In this report, we present a method for extending the original sequential state discrimination of two qubit states to a scheme of N linearly independent pure quantum states. Specifically, we obtain the conditions for the sequential state discrimination of N = 3 pure quantum states. We can analytically provide conditions when there is a special symmetry among N = 3 linearly independent pure quantum states. Additionally, we show that the scenario proposed in this study can be applied to quantum key distribution. Furthermore, we show that the sequential state discrimination of three qutrit states performs better than the strategy of probabilistic quantum cloning.

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Section: Resultsmentioning

confidence: 99%

“…Suppose that Alice prepares a quantum state out of two(or three) pure quantum states 6 – 9 , 31 – 33 .…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of Optimal Sequential State Discrimination for Linearly Independent Pure Quantum States

Namkung

Kwon

2018

Sci Rep

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“…From these, we findP opt cor (q) = (1 + l)/2(∀q ≤ q (29). The optimal POVM of q 0 = χ is unique since r opt i = 0(∀i) and {q i v i } 2 i=0 forms a triangle; see the Appendix D. This means that P I (χ) = 0.…”

Section: Proof Of Lemma Ii2 Assume That When {Qmentioning

confidence: 99%

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

Kwon

2017

Quantum Inf Process

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In this paper we consider the optimal discrimination of two mixed qubit states for a measurement that allows a fixed rate of inconclusive results. Our strategy is to transform the problem of two qubit states into a minimum error discrimination for three qubit states by adding a specific quantum state ρ0 and a prior probability q0, which behaves as an inconclusive degree. First, we introduce the beginning and the end of practical interval of inconclusive result, q (0) 0 and q (1) 0 , which are key ingredients in investigating our problem. Then we obtain the analytic form of them. Next, we show that our problem can be classified into two cases q0 = q 0 . In fact, by maximum confidences of two qubit states and non-diagonal element of ρ0, the our problem is completely understood. We provide an analytic solution of our problem when q0 = q (1) 0 , we rather supply the numerical method to find the solution, because of the complex relation between inconclusive degree and corresponding failure probability. Finally we confirm our results using previously known examples.

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Unambiguous discrimination between linearly dependent equidistant states with multiple copies

Zhang

Ren

2018

Quantum Inf Process

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Analysis of optimal unambiguous discrimination of three pure quantum states

Cited by 21 publications

References 22 publications

Analysis of Optimal Sequential State Discrimination for Linearly Independent Pure Quantum States

Analysis of Optimal Sequential State Discrimination for Linearly Independent Pure Quantum States

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

Unambiguous discrimination between linearly dependent equidistant states with multiple copies

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