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arXiv:1505.00301 · Physical Review A

Trace-distance correlations for X states and the emergence of the pointer basis in Markovian and non-Markovian regimes

Paola Concha Obando, F. M. de Paula, M. S. Sarandy

Published Sep 8, 2015• 35 citations
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Abstract

We provide analytical expressions for classical and total trace-norm (Schatten 1-norm) geometric correlations in the case of two-qubit $X$ states. As an application, we consider the open-system dynamical behavior of such correlations under phase and generalized amplitude damping evolutions. Then, we show that geometric classical correlations can characterize the emergence of the pointer basis of an apparatus subject to decoherence in either Markovian or non-Markovian regimes. In particular, as a non-Markovian effect, we obtain a time delay for the information to be retrieved from the apparatus by a classical observer. Moreover, we show that the set of initial $X$ states exhibiting sudden transitions in the geometric classical correlation has nonzero measure.

DOI
10.1103/physreva.92.032307

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We provide analytical expressions for classical and total trace-norm (Schatten 1-norm) geometric correlations in the case of two-qubit XXX states. As an application, we consider the open-system dynamical behavior of such correlations under phase and generalized amplitude damping evolutions. Then, we show that geometric classical correlations can characterize the emergence of the pointer basis of an apparatus subject to decoherence in either Markovian or non-Markovian regimes. In particular, as a non-Markovian effect, we obtain a time delay for the information to be retrieved from the apparatus by a classical observer. Moreover, we show that the set of initial XXX states exhibiting sudden transitions in the geometric classical correlation has nonzero measure.
Correlations in the open quantum systems manifest a rich phenomenology under the influence of various physical sources of noise. We theoretically study the dynamics of quantum correlations and their classical counterparts in a two-qubit system, measured by one-norm geometric quantifiers. We consider both qubits are initially prepared in the arbitrary XXX-type states and locally subjected to nonequilibrium dephasing environments with non-Markovian and nonstationary statistical features. We then explore the effects of nonequilibrium on the abrupt changes in the evolution of geometric correlations in the weak- and strong-coupling regimes. Particularly, in the weak-coupling regime, we show that the environmental nonequilibrium feature can efficiently control the appearance of double-sudden transitions and the decay rate in geometric quantum correlation dynamics. However, in the strong-coupling case, we show that the nonequilibrium nature can prolong the interval for the frozen quantum correlation and suppresses the number of multiple sudden changes in its decay rate. Moreover, the abrupt change from decay to a constant regime in classical correlation evolution reveals the emergence of the pointer-state basis. We show that the pointer-state basis appearance can be retarded in the weak-coupling case when the environment deviates from equilibrium. However, in a strong-coupling regime, we observe the metastable pointer-states basis characterized by multiple, successive sudden transitions in classical correlation dynamics. Remarkably, we unveil that the nonequilibrium feature may suppress the apparition of the metastable pointer-states basis.
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We investigate theoretically the dynamics of 1-norm geometric quantum correlations and their classical counterparts in a two-qubit system. Both qubits are initially prepared in Bell-diagonal states and locally coupled to separated thermal squeezed baths or a common squeezed thermal bath via energy-preserving interactions. We then unveil the effects of reservoir squeezing on the abrupt changes in the evolution of geometric correlations. It is found that adequately tuning the squeezing phase can efficiently suppress the dephasing rate and delay the appearance of sudden transitions in geometric correlations. Further, we show that the squeezing phase of the bath renders a different avenue to enhance the finite time interval for frozen quantum correlation. On the other hand, in this context, we show that the squeezing strength of the reservoir exhibits a negative role. In addition, in the common bath case, we observe the steady-state correlations and decoherence-free subspace, which can be governed via squeezing parameters. Moreover, the abrupt change from a decaying regime to a constant nonzero value in classical correlation signals the emergence of a pointer-state basis. We show that the emergence of a pointer-state basis can be delayed by suitably adjusting the bath squeezing parameters. Remarkably, we find the optimal value of the squeezing phase, which introduces maximum retardation in the appearance of a pointer-state basis.
We introduce the concepts of geometric classical and total correlations through Schatten 1-norm (trace norm), which is the only Schatten p -norm able to ensure a well-defined geometric measure of correlations. In particular, we derive the analytical expressions for the case of two-qubit Bell-diagonal states, discussing the superadditivity of geometric correlations. As an illustration, we compare our results with the entropic correlations, discussing both their hierarchy and monotonicity properties. Moreover, we apply the geometric correlations to investigate the ground state of spin chains in the thermodynamic limit. In contrast to the entropic quantifiers, we show that the classical correlation is the only source of 1-norm geometric correlation that is able to signal an infinite-order quantum phase transition.
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We apply the modified Brodutch and Modi method of constructing geometric measures of correlations to obtain analytical expressions for measurement-induced geometric classical and quantum correlations based on the Hellinger distance for two-qubit Bell diagonal states. Moreover, we study dynamics of the classical and quantum correlations for these states under decoherence induced by the action of bit flip, bit-phase flip, phase flip, depolarizing and generalized amplitude damping local quantum channels and identify all possible types of the decoherence dynamics. In particular, we show that these correlations exhibit freezing, sudden change and sudden transition between classical and quantum decoherence phenomena.