Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)

Chitambar, Eric; Leung, Debbie; Mančinska, Laura; Ozols, Māris; Winter, Andreas

doi:10.1007/s00220-014-1953-9

Cited by 357 publications

(389 citation statements)

References 50 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: 87%

“…While GLOBAL, SEP, and LOCC → all have this property, LOCC does not [8,9]. Hence, to properly discuss the LOCC minimum error, we must consider the class of so-called asymptotic LOCC, which is LOCC plus all its limit operations [9]. We will prove C1 with respect to this more general class of operations.…”

mentioning

confidence: 98%

“…is given by the infimum of error probabilities taken over all POVMs that can be generated by S. Note that we can replace "infimum" by "minimum" only if S is a compact set of operations. While GLOBAL, SEP, and LOCC → all have this property, LOCC does not [8,9]. Hence, to properly discuss the LOCC minimum error, we must consider the class of so-called asymptotic LOCC, which is LOCC plus all its limit operations [9].…”

mentioning

confidence: 99%

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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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supporting

confidence: 87%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Revisiting the optimal detection of quantum information

Chitambar

Hsieh

2013

Phys. Rev. A

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“…The class of Local Operations and Classical Communications [55] -LOCC operations -are general quantum opera-tions augmented with classical communication. The operations allowed are local in the sense of being restricted separately to the two parts of some bipartition of the system while potentially unlimited two-way classical communication (CC) is allowed between observers of the two regions so that operations conditioned on outcomes of the other region may be implemented.…”

Section: Differential Local Convertibility On the Ground State Manmentioning

confidence: 99%

Local convertibility of the ground state of the perturbed toric code

et al. 2014

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We present analytical and numerical studies of the behaviour of the α-Renyi entropies in the Toric code in presence of several types of perturbations aimed at studying the simulability of these perturbations to the parent Hamiltonian using local operations and classical communications (LOCC) -a property called localconvertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of α within the topological phase. From the information-theoretic point of view, this means that such ground states cannot be continuously deformed within the topological phase by means of catalyst assisted local operations and classical communications (LOCC). Such LOCC differential convertibility is on the other hand always possible in the trivial disordered phase. The non-LOCC convertibility is remarkable because it can be computed on a system whose size is independent of correlation length. This method can therefore constitute an experimentally feasible witness of topological order.

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“…Regarding a formal definition of LOCC, refer to ref. []. When LOCC is free, quantum communication of a state of an

M_{e}

‐dimensional system is achieved by LOCC assisted by a maximally entangled state

0true {| Φ_{M_{e}}^{+} ⟩}^{e} : = \frac{1}{\sqrt{M_{e}}} \sum_{l = 0}^{M_{e} - 1} {false| l false⟩}^{v_{k}} \otimes {false| l false⟩}^{v_{k^{'}}}

of the Schmidt rank

M_{e}

shared between

v_{k}

and

v_{k^{'}}

, where the superscript

e = {v_{k}, v_{k^{'}}}

represents a state shared between

v_{k}

and

v_{k^{'}}

connected by

e = {v_{k}, v_{k^{'}}}

.…”

Section: Settingsmentioning

confidence: 99%

Distributed Encoding and Decoding of Quantum Information over Networks

Yamasaki

Murao

2018

Adv Quantum Tech

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Encoding and decoding quantum information in a multipartite quantum system are indispensable for quantum error correction and also play crucial roles in multiparty tasks in distributed quantum information processing such as quantum secret sharing. To quantitatively characterize nonlocal properties of multipartite quantum transformations for encoding and decoding, we analyze the entanglement costs of encoding and decoding quantum information in a multipartite quantum system distributed among spatially separated parties connected by a network. This analysis generalizes previous studies of entanglement costs for preparing bipartite and multipartite quantum states and implementing bipartite quantum transformations by entanglement‐assisted local operations and classical communication (LOCC). We identify conditions for the parties being able to encode or decode quantum information in the distributed quantum system deterministically and exactly, when inter‐party quantum communication is restricted to a tree‐topology network. In our analysis, we reduce the multiparty tasks of implementing the encoding and decoding to sequential applications of one‐shot zero‐error quantum state splitting and merging for two parties. While encoding and decoding are inverse tasks of each other, our results suggest that a quantitative difference in entanglement cost between encoding and decoding arises due to the difference between quantum state merging and splitting.

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Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)

Cited by 357 publications

References 50 publications

Revisiting the optimal detection of quantum information

Revisiting the optimal detection of quantum information

Local convertibility of the ground state of the perturbed toric code

Distributed Encoding and Decoding of Quantum Information over Networks

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