MIXED STATE ENTANGLEMENT MEASURES FOR INTERMEDIATE SEPARABILITY

Algebraic-geometric separability criterion and low rank mixed state entanglement

We first propose a new separability criterion based on algebraicgeometric invariants of bipartite mixed states introduced in [1], then prove that for all low ranks r ≤ m+n−3, generic rank r mixed states in H A ⊗ H B have realtively high Schmidt numbers by this separability criterion (thus entangled). This also means that the algebraicgeometric separability criterion prposed here can be used to ...

Separability criteria and bounds for entanglement measures

Employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems. The separability criterion is based on a nondecomposable positive map which operates on state spaces with even dimension, N 4, and leads to a class of nondecomposable optimal entanglement witnesses. It is shown that the b...

Mixed state dense coding and its relation to entanglement measures

Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dens...

Bounding Polynomial Entanglement Measures for Mixed States

Mixed-state entanglement and quantum error correction.

Entanglement purification protocols (EPP) and quantum errorcorrecting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a bipartite mixed state M ; with a QECC, an arbitrary quantum state |ξ〉 can be transmitted at some rate Q through a noisy channel χ without degrada...