Local distinguishability of orthogonal<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>⊗</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>pure states

In this paper, we treat a local discrimination problem in the framework of asymmetric hypothesis testing. We choose a known bipartite pure state |Ψ as an alternative hypothesis, and the completely mixed state as a null hypothesis. As a result, we analytically derive an optimal type 2 error and an optimal POVM for one-way LOCC POVM and Separable POVM. For two-way LOCC POVM, we study a family of simple three-step LOCC protocols, and show that the best protocol in this family has strictly better performance than any one-way LOCC protocol in all the cases where there may exist difference between two-way LOCC POVM and one-way LOCC POVM.

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“…where |φ ⊥ d is defined by Eq. (48). By the definitions, we have cos θ = ψ|φ d , sin θ = ψ|φ ⊥ d , cos ξ = ψ|φ d /r,…”

Section: Derivation Of Analytical Solutions Of X ǫ (|ψ )mentioning

confidence: 99%

Local Hypothesis Testing Between a Pure Bipartite State and the White Noise State

Owari

Hayashi

2015

IEEE Trans. Inform. Theory

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“…It has attracted much interest in recent years, but progress has been slowed by the abundance of special cases lurking in Hilbert space. Results have been restricted mostly to low dimensional systems, specific multipartite structures, and small numbers of states [22,23,24,25]. These limitations are overcome for random states, which allow us to provide a complete generic solution for the unambiguous local distinguishability of pure states, over all multipartite quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Generic local distinguishability and completely entangled subspaces

Walgate

Scott

2008

J. Phys. A: Math. Theor.

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A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, smax, approaching the full dimension of the system, D. We show that almost all subspaces with dimension s ≤ smax are completely entangled and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n ≤ D − smax. This condition holds for almost all sets of states of all multipartite systems, and reveals something surprising. The criterion is identical for separable and for nonseparable states: entanglement makes no difference.

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“…It was shown that a set of quantum pure states are unambiguously discriminable if and only if they are linearly independent [6]. Furthermore, many variations of state discrimination problem such as local discrimination, discrimination of mixed states, discrimination of multipartite quantum states, minimum-error discrimination and asymptotic discrimination were proposed and have attracted much attention [15], [16], [17], [18], [19], [20], [? ], [?…”

Section: Introductionmentioning

confidence: 99%

Ancilla-assisted discrimination of quantum gates

Chen

Ying

2010

QIC

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The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a basic scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a d-dimensional system are perfectly discriminated with assistance from an r-dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any rd+1 quantum gates cannot be perfectly discriminated with assistance from the ancilla, and there exist rd quantum gates which can be perfectly discriminated with assistance from the ancilla. (2) The dimensionality of the minimal ancilla system is estimated. We prove that there exists a constant positive number c such that for any k\leq cr quantum gates, if they are d-assisted discriminable, then they are also r-assisted discriminable, and there are c^{\prime}rc^{\prime}>c different quantum gates which can be discriminated with a d-dimensional ancilla, but they cannot be discriminated if the ancilla is reduced to an r-dimensional system. Thus, the order O(r) of the number of quantum gates that can be discriminated with assistance from an r-dimensional ancilla is optimal. The results reported in this paper represent a preliminary step toward understanding the role ancilla system plays in discrimination of quantum gates as well as the power and limit of superdense coding.

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Local distinguishability of orthogonal2⊗3pure states

Cited by 30 publications

References 31 publications

Local Hypothesis Testing Between a Pure Bipartite State and the White Noise State

Local Hypothesis Testing Between a Pure Bipartite State and the White Noise State

Generic local distinguishability and completely entangled subspaces

Ancilla-assisted discrimination of quantum gates

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