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.
Categories: quant-ph