Analytical formula connecting entangled state and the closest disentangled state

Abstract

The separable state closest to a given entangled state in the relative entropy measure is called the closest disentangled state. We provide an analytical formula connecting the entangled state and the closest disentangled state in two qubits. Using this formula, when any disentangled state ($\sigma$) located at the entangle-disentangle boundary is given, entangled states to which $\sigma$ is closest can be obtained analytically. Further, this formula naturally defines the direction normal to the boundary surface. The direction is uniquely determined by $\sigma$ in almost all cases.

4 pages. minor correction, refs were added

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• Relative entropy of entanglement for certain multipartite mixed states
• An Introduction to Quantum Entanglement: a Geometric Approach
• Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting
• Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states
• Comparison of the relative entropy of entanglement and negativity
• On convex optimization problems in quantum information theory
• Direct evaluation of pure graph state entanglement
• Entanglement in pure and thermal cluster states
• Relative entropy of entanglement of a kind of two qubit entangled states
• Direct-dynamical entanglement-discord relations
• Representations of two-qubit and ququart states via discrete Wigner functions