Quantifying Entanglement

Neha Pathania, Tabish Qureshi

Carlen, Eric

Ivan Šupić, Paul Skrzypczyk, Daniel Cavalcanti

In a previous work [Phys. Rev. Lett. 119, 110501] we proved that every entangled quantum state can be used to implement a non-classical teleportation channel. Here we turn to the question of quantifying how non-classical these channels are. We define several quantifiers of non-classical teleportation which can be computed using semidefinite programming. Furthermore, we prove quantitative relations between these quantifiers and the amount of entanglement in the underlying states. Apart from providing further insight on the relation between teleportation and entanglement, our work introduces a method to estimate entanglement in a teleportation experiment.

James Schneeloch, Richard J. Birrittella, Christopher C. Tison +3 more

In this work, we provide a means to quantify genuine tripartite entanglement in arbitrary (pure and mixed) continuous-variable states as measured by the tripartite entanglement of formation---a resource-based measure quantifying genuine multipartite entanglement in units of elementary Greenberger-Horne-Zeilinger (GHZ) states called gebits. Furthermore, we predict its effectiveness in quantifying the tripartite spatial and energy-time entanglement in photon triplets generated in cascaded spontaneous parametric down-conversion (SPDC), and find that ordinary nonlinear optics can be a substantial resource of tripartite entanglement.

Zong‐Wen Yu, Su Hu, Chunlei Zhang

In this paper, we consider the problem of how to quantify entanglement for any multipartite quantum states. For bipartite pure states partial entropy is a good entanglement measure. By using partial entropy, we firstly introduce the Combinatorial Entropy of Fully entangled states (CEF) which can be used to quantify entanglement for any fully entangled pure states. In order to quantify entanglement for any multipartite states we also need another concept the Entanglement Combination (EC) which can be used to completely describe the entanglement between any parties of the given quantum states. Combining CEF with EC, we define the Combinatorial Entropy (CE) for any multipartite pure states and present some nice properties which indicate CE is a good entanglement measure. Finally, we point out the feasibility of extending these three concepts to mixed quantum states.

Vlatko Vedral, Martin Bodo Plenio, P. L. Knight