Characteristics and benchmarks of entanglement of mixed states -- the two qubit case

Details Characteristics and benchmarks of entanglement of mixed states -- the two qubit case Characteristics and benchmarks of entanglement of mixed states -- the two qubit case

2008-01-10

arxiv.org/abs/0801.1545v1

Physics

Quantum Physics

12 pages, 6 figures. Enlarged version of quant-phy/0703017

Scientific paper

10.1103/PhysRevA.77.022322

We propose that the entanglement of mixed states is characterised properly in terms of a probability density function $\mathcal{P}_{\rho}(\mathcal{E})$. There is a need for such a measure since the prevalent measures (such as \textit{concurrence} and \textit{negativity}) for two qubit systems are rough benchmarks, and not monotones of each other. Focussing on the two qubit states, we provide an explicit construction of $\mathcal{P}_{\rho}(\mathcal{E})$ and show that it is characterised by a set of parameters, of which concurrence is but one particular combination. $\mathcal{P}_{\rho}(\mathcal{E})$ is manifestly invariant under $SU(2) \times SU(2)$ transformations. It can, in fact, reconstruct the state up to local operations - with the specification of at most four additional parameters. Finally the new measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.

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