Entanglement detection using majorization uncertainty bounds

Positive maps, majorization, entropic inequalities, and detection of entanglement

In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map Λ : Md(C) → Md(C) can be written as the difference between two completely positive maps Λ = Λ1 − Λ2, we propose a possible way to generalize...

Majorization entropic uncertainty relations

Zbigniew Puchała, Łukasz Rudnicki, Karol Życzkowski Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland Freiburg Insitute for Advanced Studies, Alb...

Majorization bounds for signless Laplacian eigenvalues

Continuity bounds for entanglement

To flesh out the notion that entanglement is a resource, various measures of entanglement have been proposed to quantify the amount of entanglement shared between two or more quantum systems. For a pure state of a twoparty quantum system, Popescu and Rohrlich [6] and Vidal [7] have shown that the measure of entanglement is uniquely specified by certain natural axioms: it is given by the von Neu...

Collective uncertainty entanglement test.

For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled states and it allows us to construct a family of entanglement measures, we shall call collect...