Locally accessible information and distillation of entanglement (5 pages)

Igor Devetak

M. Popp, Frank Verstraete, Miguel Angel Martin-Delgado

Sibasish Ghosh A, Pramod S. Joag, Guruprasad Kar +2 more

A different type of complementarity relation is found between locally accessible information and final average entanglement for a given ensemble. It is also shown that in some well-known distillation protocols, this complementary relation is optimally satisfied. We discuss the interesting trade-off between locally accessible information and distillable entanglement for some states.

Mankei Tsang, Demetri Psaltis

Aditi Sen, Ujjwal Sen, Maciej Lewenstein

We find a universal lower bound on locally accessible information for arbitrary bipartite quantum ensembles, when one of the parties is two dimensional. In higher dimensions and in a higher number of parties, the bound is on accessible information by separable operations. We show that for any given density matrix (of an arbitrary number of parties and dimensions), there exists an ensemble, which averages to the given density matrix and whose locally accessible information saturates the lower bound. Moreover, we give a general method to obtain bounds on the yield of singlets in distillation protocols that involves local distinguishing, by using lower and upper bounds on locally accessible information. We then illustrate it by using our lower bound, along with a previously obtained upper bound, on locally accessible information.

Takato Mori, Beni Yoshida

A bstract The Ryu-Takayanagi formula predicts that two boundary subsystems A and C can exhibit large mutual information I ( A : C ) even when they are spatially disconnected on the boundary and separated by a buffer subsystem B , as long as A and C have connected entanglement wedge in the bulk. However, whether the reduced state ρ AC contains distillable EPR pairs has remained a longstanding open problem. In this work, we resolve this problem by showing that: i) there is no LO-distillable entanglement at leading order in G N , suggesting the absence of bipartite entanglement in a holographic mixed state ρ AC , and ii) one-shot, one-way LOCC-distillable entanglement is given at leading order by locally accessible information J W ( A | C ), which is related to the entanglement wedge cross section E W involving the (third) purifying system B via J W ( A | C ) = S A − E W ( A : B ). Namely, we demonstrate that a connected entanglement wedge does not necessarily imply nonzero distillable entanglement in one-shot, one-way LOCC. We also show that entanglement of formation E F ( A : C ) is given by E W ( A : C ) at leading order in holography.