Concurrence versus purity: Influence of local channels on Bell states of two qubits

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Authors

ZIMAN Mário BUŽEK Vladimír

Year of publication 2005
Type Article in Periodical
Magazine / Source Physical Review A
MU Faculty or unit

Faculty of Informatics

Citation
Field Theoretical physics
Keywords concurrence; entanglement; local dynamics; decoherence
Description We analyze how a maximally entangled state of two qubits (e.g., the singlet $psi_s$) is affected by the action of local channels described by completely positive maps $E$. We analyze the concurrence and the purity of states $rho_E=E \otimes I_psi_s$. Using the concurrence-versus-purity phase diagram we characterize local channels $E$ by their action on the singlet state $psi_s$. We specify a region of the concurrence-versus-purity diagram that is achievable from the singlet state via the action of unital channels. We show that even the most general (including nonunital) local channels acting just on a single qubit of the original singlet state cannot generate the maximally entangled mixed states. We study in detail various time evolutions of the original singlet state induced by local Markovian semigroups. We show that the decoherence process is represented in the concurrence-versus-purity diagram by a line that forms the lower bound of the achievable region for unital maps. On the other hand, the depolarization process is represented by a line that forms the upper bound of the region of maps induced by unital maps.
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