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Register a new userMonogamy Inequality and Residual Entanglement of Three Qubits under Decoherence
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Thiago Rodrigues de Oliveira
Publication date
2009
fields
Physics
and research's language is
English
Authors
Thiago R. de Oliveira
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Exploring an analytical expression for the convex roof of the pure state squared concurrence for rank 2 mixed states the entanglement of a system of three particles under decoherence is studied, using the monogamy inequality for mixed states and the residual entanglement obtained from it. The monogamy inequality is investigated both for the concurrence and the negativity in the case of local independent phase damping channel acting on generalized GHZ states of three particles and the local independent amplitude damping channel acting on generalized W state of three particles. It is shown that the bipartite entanglement between one qubit and the rest has a qualitative similar behavior to the entanglement between individual qubits, and that the residual entanglement in terms of the negativity cannot be a good entanglement measure for mixed states, since it can increase under local decoherence.
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We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.
We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the two cases (I) two independent bosonic baths and (II) one common bath, at temperature T. The entanglement dynamics is studied in terms of the concurrence C (t) between the two spins and of the von Neumann entropy S(t) with respect to the bath, as a function of time. We prove that the system does thermalize. In the case (II) of a single bath, the existence of a decoherence-free (DFS) subspace makes entanglement dynamics very rich. We show that when the system is initially in a state with a component in the DFS the relaxation time is surprisingly long, showing the existence of semi-decoherence free subspaces. The equilibrium state in this case is not the Gibbs state. The entanglement dynamics for the single bath case is also studied as a function of temperature, coupling strength with the environment and strength of tunneling coupling. The case of the mixed state is finally shown and discussed.
The monogamy inequality in terms of the concurrence, called the Coffman-Kundu-Wootters inequality [Phys. Rev. A {bf 61}, 052306 (2000)], and its generalization [T.J. Osborne and F. Verstraete, Phys. Rev. Lett. {bf 96}, 220503 (2006)] hold on general $n$-qubit states including mixed ones. In this paper, we consider the monogamy inequalities in terms of the fully entangled fraction and the teleportation fidelity. We show that the monogamy inequalities do not hold on general mixed states, while the inequalities hold on $n$-qubit pure states.
It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.
We analyze the entanglement distribution and the two-qubit residual entanglement in multipartite systems. For a composite system consisting of two cavities interacting with independent reservoirs, it is revealed that the entanglement evolution is restricted by an entanglement monogamy relation derived here. Moreover, it is found that the initial cavity-cavity entanglement evolves completely to the genuine four-partite cavities-reservoirs entanglement in the time interval between the sudden death of cavity-cavity entanglement and the birth of reservoir-reservoir entanglement. In addition, we also address the relationship between the genuine block-block entanglement form and qubit-block form in the interval.
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