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 states 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.

• Received 21 January 2003

DOI:https://doi.org/10.1103/PhysRevA.67.060301