Asymptotically perfect discrimination in the local-operation-and-classical-communication paradigm

Kleinmann, Matthias; Kampermann, Hermann; Bruß, Dagmar

doi:10.1103/physreva.84.042326

Cited by 47 publications

(61 citation statements)

References 19 publications

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“…A primary motivation for studying this problem is to better understand the limitations of processing quantum information by LOCC. Our results complement a series of recent results in this direction [9,16,18]. Theorem 1 largely extends the work of Ref.…”

supporting

confidence: 77%

“…Theorem 1 largely extends the work of Ref. [16] as we reduce asymptotic minimum error discrimination of linearly independent states to asymptotic perfect discrimination. Asymptotic LOCC is not just a technical consideration, but rather it arises from very practical situations.…”

mentioning

confidence: 78%

“…[15] provides simple criteria for deciding perfect LOCC distinguishability of two-qubit ensembles, no analogous criteria exists for asymptotic LOCC. The only general result for asymptotic discrimination has been recently obtained by Kleinmann et al [16]. Here we cite their result in its strongest form, adapted specifically for the problem at hand.…”

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confidence: 96%

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Revisiting the optimal detection of quantum information

Chitambar

Hsieh

2013

Phys. Rev. A

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In 1991, Peres and Wootters wrote a seminal paper on the nonlocal processing of quantum information [Phys. Rev. Lett. 66, 1119(1991]. We return to their classic problem and solve it in various contexts. Specifically, for discriminating the "double trine" ensemble with minimum error, we prove that global operations are more powerful than local operations with classical communication (LOCC). Even stronger, there exists a finite gap between the optimal LOCC probability and that obtainable by separable operations (SEP). Additionally we prove that a two-way, adaptive LOCC strategy can always beat a one-way protocol. Our results demonstrate "nonlocality without entanglement" in two-qubit pure states. One physical restriction that naturally emerges in quantum communication scenarios is nonlocality. Here, two or more parties share some multipart quantum system, but their subsystems remain localized with no "global" quantum interactions occurring between them. Instead, the system is manipulated through local quantum operations and classical communication (LOCC) performed by the parties.Peres and Wootters were the first to introduce the LOCC paradigm and study it as a restricted class of operations in their seminal work [1]. To gain insight into how the LOCC restriction affects information processing, they considered a seemingly simple problem. Suppose that Alice and Bob each possess a qubit, and with equal probability, their joint system is prepared in one of the states belonging to the set {|D i = |s i ⊗ |s i } 2 i=0 , where |s i = U i |0 and U = exp(− iπ 3 σ y ). This highly symmetric ensemble is known as the "double trine," and we note that lying orthogonal to all three states is the singlet | − = √ 1/2(|01 − |10 ). Alice and Bob's goal is to identify which double trine element was prepared only by performing LOCC. Like any quantum operation used for state identification, Alice and Bob's collective action can be described by some positiveoperator valued measure (POVM). While the nonorthogonality of the states prohibits the duo from perfectly identifying their state, there are various ways to measure how well they can do. Peres and Wootters chose the notoriously difficult measure of accessible information [2], but their paper raises the following two general conjectures concerning the double trine ensemble, which can apply to any measure of distinguishability: (C1) LOCC is strictly suboptimal compared to global operations. (C2) The optimal LOCC protocol involves two-way communication and adaptive measurements.The set of global POVMs will be denoted by GLOBAL, and C1 can be symbolized by GLOBAL > LOCC. A two-way LOCC protocol with adaptive measurement refers to at least three rounds of measurement, Alice → Bob → Alice, with the choice of measurement in each round depending on the * echitamb@siu.edu † Min-Hsiu.Hsieh@uts.edu.au

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confidence: 77%

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confidence: 78%

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Revisiting the optimal detection of quantum information

Chitambar

Hsieh

2013

Phys. Rev. A

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“…They also thank Nathaniel Johnston for his comments, particularly for making them aware of asymptotic distinguishability from [12].…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…A sightly stronger result on asymptotic distinguishability is obtained from [12], which allows the parties to have infinite resources and arbitrarily long times in their LOCC protocol. Proposition 2 of [12] implies that even under asymptotic LOCC, perfect discrimination is only possible for the UOB that belong to the maximum dimensional family.…”

Section: Distinguishability By Local Operations and Classical Commentioning

confidence: 99%

Local distinguishability of generic unentangled orthonormal bases

2016

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An orthonormal basis consisting of unentangled (pure tensor) elements in a tensor product of Hilbert spaces is an Unentangled Orthogonal Basis (UOB). In general, for n qubits, we prove that in its natural structure as a real variety, the space of UOB is a bouquet of products of Riemann spheres parametrized by a class of edge colorings of hypercubes. Its irreducible components of maximum dimension are products of 2 n − 1 two-spheres. Using a theorem of Walgate and Hardy, we observe that the UOB whose elements are distinguishable by local operations and classical communication (called locally distinguishable or LOCC distinguishable UOB) are exactly those in the maximum dimensional components. Bennett et al, in their in-depth study of quantum nonlocality without entanglement, include a specific 3 qubit example UOB which is not LOCC distinguishable; we construct certain generalized counterparts of this UOB in n qubits.

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Statistical Methods for Quantum State Verification and Fidelity Estimation

Shang

Gühne

2022

Adv Quantum Tech

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The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource‐efficient manner. In this article, a review of the recent progress in this field is presented. How the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing is explained first. Then, various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication are explained in detail. Finally, several extensions of the problem, such as the certification of quantum channels and the verification of entanglement are discussed.

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Asymptotically perfect discrimination in the local-operation-and-classical-communication paradigm

Cited by 47 publications

References 19 publications

Revisiting the optimal detection of quantum information

Revisiting the optimal detection of quantum information

Local distinguishability of generic unentangled orthonormal bases

Statistical Methods for Quantum State Verification and Fidelity Estimation

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