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Local filtering operations on two qubits

Frank Verstraete·Jeroen Dehaene·Bart De Moor
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Abstract

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 $ρ'\sim (A\otimes B)ρ(A\otimes B)^{\dagger}$. We consider a real matrix parameterization 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 filterin operations for concentrating entanglement. Furthermore we give a complete characterization of the mixed states that can be purified arbitrary close to a Bell state. Finally we obtain a new way of calculating the entanglement of formation.

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Frank Verstraete, Jeroen Dehaene, Bart De Moor. 2000-11-28. Local filtering operations on two qubits. https://doi.org/10.1103/physreva.64.010101

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