Local filtering operations on two qubits

By Frank Verstraete, Jeroen Dehaene, B. De Moor. 2000

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We consider one single copy of a mixed state of two qubits and investigate how its entanglement changes under local quantum operations and classical communications (LQCC) of the type ${\ensuremath{\rho}}^{\ensuremath{'}}\ensuremath{\sim}(A\ensuremath{\bigotimes}B)\ensuremath{\rho}(A\ensuremath{\bigotimes}{B)}^{\ifmmode\dagger\else\textdagger\fi{}}.$ We consider a real matrix parametrization of the set of density matrices and show that these LQCC operations correspond to left and right multiplication by a Lorentz matrix, followed by normalization. A constructive way of bringing this matrix into a normal form is derived. This allows us to calculate explicitly the optimal local filtering operations for concentrating entanglement. Furthermore, we give a complete characterization of the mixed states that can be purified arbitrarily close to a Bell state. Finally, we obtain a new way of calculating the entanglement of formation.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c45a1772f14403c36acd47e6679a6ffa7bdb4306