Characteristics and benchmarks of entanglement of mixed states: The two-qubit case

Abstract

We propose that the entanglement of mixed states is characterized properly in terms of a probability density function [script P]rho([script E]). There is a need for such a measure since the prevalent measures (such as concurrence and negativity) for two-qubit systems are rough benchmarks and not monotones of each other. Focusing on the two-qubit states, we provide an explicit construction of [script P]rho([script E]) and show that it is characterized by a set of parameters of which concurrence is but one particular combination. [script P]rho([script E]) is manifestly invariant under SU(2)×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 measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.