The structural physical approximation conjecture

Shultz, Fred

doi:10.1063/1.4938226

Cited by 11 publications

(22 citation statements)

References 72 publications

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“…[29] that SPAed maps to optimal positive maps correspond to entanglement-breaking channels. While there have been a number of supporting examples [29,30,31,32,33,34,35], counterexamples have been finally found, firstly in indecomposable cases [36,37] and then decomposable cases [38], see also numerical evidences [74] and a recent review [45]. In the following, we address the conjecture with an observation on no-go theorems in quantum theory and overview the progress.…”

Section: Structural Physical Approximation and Quantum Channelsmentioning

confidence: 99%

“…We also refer to the excellent reviews on the mathematical structure of the conjecture and the counterexamples [45] and on the detailed terms of optimality, extremality, atomicity, and facial structures of EWs [72,66]. The counterexample for indecomposable cases is given in Ref.…”

Section: Structural Physical Approximation and Quantum Channelsmentioning

confidence: 99%

“…It turns out that SPA can introduce the so-called quantum design [42,43,44], a specific form of POVMs, that is of both fundamental and practical interest in quantum information theory. Recently, an excellent review has been presented with a focus on the mathematical structure of SPA and the conjecture [45].…”

Section: Introductionmentioning

confidence: 99%

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Designing quantum information processing via structural physical approximation

Bae

2017

Rep. Prog. Phys.

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In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those nonphysical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.

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Section: Structural Physical Approximation and Quantum Channelsmentioning

confidence: 99%

Section: Structural Physical Approximation and Quantum Channelsmentioning

confidence: 99%

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Designing quantum information processing via structural physical approximation

Bae

2017

Rep. Prog. Phys.

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“…We now introduce the set of extremal semiquantum witnessing games (ESQWGs), W e sq ⊂ W sq , which correspond to EEWs. This class of games is necessary and sufficient for entanglement detection, since for every entangled state there exists an EEW which detects it [30,31] …”

Section: An Extremal Ew (Eew)ŵmentioning

confidence: 99%

“…e is one that cannot be written as a convex combination of any two other block-negative operators, and hence, there exists a pure product state ja; bi ∈ S sep such that ha; bjŴ e ja; bi ¼ 0 [30,31]. We now introduce the set of extremal semiquantum witnessing games (ESQWGs), W e sq ⊂ W sq , which correspond to EEWs.…”

Section: An Extremal Ew (Eew)ŵmentioning

confidence: 99%

Measurement-Device-Independent Approach to Entanglement Measures

2017

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Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here, we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context, a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the local operations and classical communication paradigm. Second, we prove that the maximum payoff for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states. DOI: 10.1103/PhysRevLett.118.150505 Introduction.-Entanglement is a valuable resource for practical as well as fundamental applications of quantum theory, ranging from quantum computation and communication to metrology [1-3]. There are two major challenges in understanding entanglement that stimulates this research. First, it is extremely difficult to specify all the nonentangled bipartite or multipartite quantum states. In fact, the problem is known to be NP-hard [4,5]. Second, not surprisingly, the characterization of entangled states, i.e., the quantification of entanglement within quantum states, is an equally difficult task. The answer to the second challenge is practically very important because it tells us how well our protocols will perform using a given state [6][7][8][9].Focusing on the second challenge above, a first level of hardness is that the quantification of entanglement using almost any entanglement measure, e.g., entanglement of formation [10], negativity [11,12], or random robustness [13], requires estimating a large number of density matrix elements, a task which is difficult to perform on bipartite and multipartite quantum states. While this difficulty can be partially circumvented by making use of entanglement witnesses (EWs) when lower bounds on the entanglement are desired [14][15][16][17][18][19], errors and misalignments of the measurement devices can still lead to incorrect estimations of the quantities and thus, erroneous conclusions. A measurementdevice-independent approach is therefore desirable.Recent work by Buscemi [20] has introduced a new way to think about entanglement detection [21][22][23][24]. The idea is to map the problem onto a modified class of nonlocal games, called semiquantum nonlocal games (SQNLGs). In any such game, two players (Alice and Bob) share a possibly entangled state. A referee (Charlie) starts by asking them

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The Resource Theory of Entanglement

Shähandeh

2019

Springer Theses

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The structural physical approximation conjecture

Cited by 11 publications

References 72 publications

Designing quantum information processing via structural physical approximation

Designing quantum information processing via structural physical approximation

Measurement-Device-Independent Approach to Entanglement Measures

The Resource Theory of Entanglement

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