``Squashed entanglement'': An additive entanglement measure
Abstract
In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the socalled intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call "squashed entanglement": it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general. Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannestype inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 March 2004
 DOI:
 10.1063/1.1643788
 arXiv:
 arXiv:quantph/0308088
 Bibcode:
 2004JMP....45..829C
 Keywords:

 03.65.Ud;
 02.10.v;
 03.67.Dd;
 Entanglement and quantum nonlocality;
 Logic set theory and algebra;
 Quantum cryptography;
 Quantum Physics
 EPrint:
 8 pages, revtex4. v2 has some more references and a bit more discussion, v3 continuity discussion extended, typos corrected