Exact Calculation of Robustness of Entanglement via Convex Semi-Definite Programming

Jafarizadeh, M. A.; Mirzaee, M.; Rezaee, Mousa

doi:10.1142/s0219749905001043

Cited by 11 publications

(13 citation statements)

References 35 publications

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“…These results allow us to obtain nontrivial bounds for resource trading in specific theories by computing the modification coefficients (which can be efficiently done in many cases [9,[67][68][69][70][71][72]). For example, the golden coefficients of coherence, entanglement and purity theories induce bounds directly given by the smooth resource measures without modification, which is consistent with previous results [44,46,47,73].…”

Section: Optimal Rates Of One-shot Resource Manipulationmentioning

confidence: 99%

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One-Shot Operational Quantum Resource Theory

2019

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A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint, the optimal efficiency of resource formation and distillation tasks with only a single copy of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation. We find general bounds on the optimal rates characterized by resource measures based on the smooth max/min-relative entropies and hypothesis testing relative entropy, as well as the free robustness measure, providing them with general operational meanings in terms of optimal state conversion. Our results encompass a wide class of resource theories via the theory-dependent coefficients we introduce, and the discussions are solidified by important examples, such as entanglement, coherence, superposition, magic states, asymmetry, and thermal

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Section: Optimal Rates Of One-shot Resource Manipulationmentioning

confidence: 99%

“…We also note that the resource measures considered in this work often admit efficient SDP formulation [9,71] as well as analytical expressions [9,[67][68][69][70]72], which make our bounds of practical use in many important circumstances.…”

Section: Optimal Rates Of One-shot Resource Manipulationmentioning

confidence: 99%

One-Shot Operational Quantum Resource Theory

2019

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“…In this section, we are motivated by the following fact: it is important to have efficiently computable quantifications of quantum resources. A convex optimization problem constrained by semidefinite matrix inequalities is called a semidefinite program (SDP) [26]; they are efficiently computable, and appear frequently in quantum information theory [8,15,28]. In fact, entanglement measures are often defined via suitable optimization [14].…”

Section: Incompatibility Monotones Via Semidefinite Programmentioning

confidence: 99%

Noise robustness of the incompatibility of quantum measurements

2015

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The existence of incompatible measurements is a fundamental phenomenon having no explanation in classical physics. Intuitively, one considers given measurements to be incompatible within a framework of a physical theory, if their simultaneous implementation on a single physical device is prohibited by the theory itself. In the mathematical language of quantum theory, measurements are described by POVMs (positive operator valued measures), and given POVMs are by definition incompatible if they cannot be obtained via coarse-graining from a single common POVM; this notion generalizes noncommutativity of projective measurements. In quantum theory, incompatibility can be regarded as a resource necessary for manifesting phenomena such as Clauser-Horne-Shimony-Holt (CHSH) Bell inequality violations or Einstein-Podolsky-Rosen (EPR) steering which do not have classical explanation. We define operational ways of quantifying this resource via the amount of added classical noise needed to render the measurements compatible, i.e., useless as a resource. In analogy to entanglement measures, we generalize this idea by introducing the concept of incompatibility measure, which is monotone in local operations. In this paper, we restrict our consideration to binary measurements, which are already sufficient to explicitly demonstrate nontrivial features of the theory. In particular, we construct a family of incompatibility monotones operationally quantifying violations of certain scaled versions of the CHSH Bell inequality, prove that they can be computed via a semidefinite program, and show how the noise-based quantities arise as special cases. We also determine maximal violations of the new inequalities, demonstrating how Tsirelson's bound appears as a special case. The resource aspect is further motivated by simple quantum protocols where our incompatibility monotones appear as relevant figures of merit.

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“…All the measures mentioned in the main text use semidefinite cones, as already noted by various authors [12,21,60,61]. Building upon the conic linear form detailed in Appendix B, we provide below practical recipes to construct entanglement measure cones.…”

Section: Appendix B: Conic Linear Programsmentioning

confidence: 99%

Practical measurement-device-independent entanglement quantification

et al. 2018

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The robust estimation of entanglement is key to the validation of implementations of quantum systems. On the one hand, the evaluation of standard entanglement measures, either using quantum tomography or using quantitative entanglement witnesses requires perfect implementation of measurements. On the other hand, measurement-device-independent entanglement witnesses (MDIEWs) can certify entanglement of all entangled states using untrusted measurement devices. We show that MDIEWs can be used as well to quantify entanglement according to standard entanglement measures, and present a practical method to derive such witnesses using experimental data only.

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Exact Calculation of Robustness of Entanglement via Convex Semi-Definite Programming

Cited by 11 publications

References 35 publications

One-Shot Operational Quantum Resource Theory

One-Shot Operational Quantum Resource Theory

Noise robustness of the incompatibility of quantum measurements

Practical measurement-device-independent entanglement quantification

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