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

Abstract

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.

arXiv comment12 pages, 6 figures. Enlarged version of quant-phy/0703017

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• Dynamics of entanglement in Two-Qubit Open System Interacting with a Squeezed Thermal Bath via Dissipative interaction
• Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons
• Entanglement Dynamics in Two-Qubit Open System Interacting with a Squeezed Thermal Bath via Quantum Nondemolition interaction
• Classical simulation of entangled states
• Tomography, Control and Characterization of Entanglement in Three level Atomic System
• Optimal observables to determine entanglement of a two qubit state
• Dynamics of Quantum Coherence and Non-Classical Correlations in Open Quantum System Coupled to a Squeezed Thermal Bath