Bounds on localizable information via semidefinite programming

Synak-Radtke, Barbara; Horodecki, Karol; Horodecki, Michał

doi:10.1063/1.2000707

Cited by 7 publications

(3 citation statements)

References 22 publications

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“…But, on the other hand, it is much harder to evaluate. Some bounds on the regularized quantum deficit have been obtained in [8]. In our case we consider one copy version of quantum deficit and additionally we allow only for a special kind of protocols of localizing information into a subsystem.…”

Section: Introductionmentioning

confidence: 99%

Can quantum correlations be completely quantum?

Pańkowski

Synak-Radtke

2008

J. Phys. A: Math. Theor.

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Deficit of information zero-way was proposed in [1] as one of possible measures of quantumness of correlations. Numerical calculations suggested that there exist such states for which this quantity is almost equal to mutual information. In this paper we present a family of states for which we have equality between above measure of quantumness of correlations and the measure of total correlations -mutual information. It means that whole correlations in these states have, in some sense, quantum character and that quantum correlations do not necessarily imply classical correlations. We prove this intriguing feature for a subclass of 2 ⊗ 2 separable states. We also present numerical result suggesting that this interesting situation might also happen for 2 ⊗ 2 entangled states.

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Section: Introductionmentioning

confidence: 99%

Can quantum correlations be completely quantum?

Pańkowski

Synak-Radtke

2008

J. Phys. A: Math. Theor.

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“…In the specific case of V = U , it is well known that the unique solution of equation (19) is provided by the multidimensional Werner states [16]. For two qudits A and B (with the same dimension d), the Werner states are defined by the one-parameter class [16,41] ρ AB (µ) :…”

Section: Qudits In Multidimensional Twirling Environmentsmentioning

confidence: 99%

Entanglement reactivation in separable environments

Pirandola

2013

New J. Phys.

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Combining two entanglement-breaking channels into a correlatednoise environment restores the distribution of entanglement. Surprisingly, this reactivation can be induced by the injection of separable correlations from the composite environment. In any dimension (finite or infinite), we can construct classically correlated 'twirling' environments which are entanglement-breaking in the transmission of single systems but entanglement-preserving when two systems are transmitted. Here entanglement is simply preserved by the existence of decoherence-free subspaces. Remarkably, even when such subspaces do not exist, a fraction of the input entanglement can still be distributed. This is found in separable Gaussian environments, where distillable entanglement is able to survive the two-mode transmission, despite being broken in any single-mode transmission by the strong thermal noise. In the Gaussian setting, entanglement restoration is a threshold process, occurring only after a critical amount of correlations has been injected. Such findings suggest new perspectives for distributing entanglement in realistic environments with extreme decoherence, identifying separable correlations and classical memory effects as physical resources for 'breaking entanglement-breaking'.

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“…one can define a quantity, which is not an entanglement measure, but may be useful (see [22] in this context):…”

Section: Example 2 Consider the Statementioning

confidence: 99%

On quantum advantage in dense coding

Horodecki¹,

Piani²

2012

J. Phys. A: Math. Theor.

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Abstract-The quantum advantage of dense coding is studied, considering general encoding quantum operations. Particular attention is devoted to the case of many senders, and it is shown that restrictions on the possible operations on the senders' side may make some quantum state useless for dense-coding. It is shown, e.g., that some states are useful for dense coding if the senders can communicate classically (but not quantumly), yet they cannot be used for dense coding, if classical communication is not allowed. These no-go results are actually independent of the particular quantification of the quantum advantage, being valid for any reasonable choice. It is further shown that the quantum advantage of dense coding satisfies a monogamy relation with the so-called entanglement of purification.Index Terms-dense coding, quantum advantage, monogamy of correlations, multipartite entanglement, entanglement of purification

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Bounds on localizable information via semidefinite programming

Cited by 7 publications

References 22 publications

Can quantum correlations be completely quantum?

Can quantum correlations be completely quantum?

Entanglement reactivation in separable environments

On quantum advantage in dense coding

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