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Search Results (3)

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Keywords = disentangled evolution operators

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23 pages, 1358 KB  
Article
Disentanglement Dynamics in Nonequilibrium Environments
by Mingli Chen, Haonan Chen, Tao Han and Xiangji Cai
Entropy 2022, 24(10), 1330; https://doi.org/10.3390/e24101330 - 21 Sep 2022
Cited by 9 | Viewed by 2092
Abstract
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the [...] Read more.
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments. Full article
(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)
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15 pages, 1831 KB  
Article
Single-Qubit Driving Fields and Mathieu Functions
by Marco Enríquez, Alfonso Jaimes-Nájera and Francisco Delgado
Symmetry 2019, 11(9), 1172; https://doi.org/10.3390/sym11091172 - 16 Sep 2019
Cited by 2 | Viewed by 4556
Abstract
We report a new family of time-dependent single-qubit radiation fields for which the correspondent evolution operator can be disentangled in an exact way via the Wei–Norman formalism. Such fields are characterized in terms of the Mathieu functions. We show that the regions of [...] Read more.
We report a new family of time-dependent single-qubit radiation fields for which the correspondent evolution operator can be disentangled in an exact way via the Wei–Norman formalism. Such fields are characterized in terms of the Mathieu functions. We show that the regions of stability of the Mathieu functions determine the nature of the driving fields: For parameters in the stable region, the fields are oscillating, being able to be periodic under certain conditions. Whereas, for parameters in the instability region, the fields are pulse-like. In addition, in the stability region, this family admits solutions for evolution loops in quantum control. We obtain some prescriptions to reach such a control effect. Geometric phases in the evolution are also analyzed and discussed. Full article
(This article belongs to the Special Issue Quantum Information and Symmetry)
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15 pages, 1647 KB  
Article
Exactly Solvable One-Qubit Driving Fields Generated via Nonlinear Equations
by Marco Enríquez and Sara Cruz y Cruz
Symmetry 2018, 10(11), 567; https://doi.org/10.3390/sym10110567 - 1 Nov 2018
Cited by 10 | Viewed by 2713
Abstract
Using the Hubbard representation for S U ( 2 ) , we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of nonlinear coupled equations. In order to [...] Read more.
Using the Hubbard representation for S U ( 2 ) , we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of nonlinear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. A physical model with the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomenon. Full article
(This article belongs to the Special Issue Symmetry Breaking in Quantum Phenomena)
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