Dynamics of quantum discord of two coupled spin-1/2’s subjected to time-dependent magnetic fields

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This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling two-level system, which is in turn coupled to a harmonic mode (i.e., the molecule). A decay operator acting on the two-level system describes phenomenologically probability losses. Finally, the temperature of the molecule is controlled by means of a Nosé-Hoover chain thermostat. A numerical study of the quantum dynamics of this toy model at different temperatures is reported. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction. The possibility that the formalism here presented can be extended to treat both more quantum states (∼10) and many more classical modes or atomic particles (∼103−105) is highlighted.

Section: Discussionmentioning

confidence: 99%

Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature

Grimaldi

Sergi

Messina

2021

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“…The symmetry properties of our time-dependent Hamiltonian model play a crucial role since it guarantees that an initial X density matrix evolves keeping such a structure at any time instant and, on the other hand, that the quantum discord of such a state could be analytically determined [ 50 ]. This is why we choose an X state as initial condition and in this class we concentrate on generic

-parametric Werner states.…”

Section: Discussionmentioning

confidence: 99%

“…An interesting dynamical property of the Hamiltonian model consists of the fact that the X structure of an initial state is preserved during the evolution [ 50 ]. Indeed, suppose that the two-spin-1/2 system is initially prepared in a general X state, as given by Equation ( 4 ).…”

Section: Time-dependent Hamiltonian Model and The Related Evolutiomentioning

confidence: 99%

“…Others, instead, show the dynamical evolution of concurrence and quantum discord, generated in a chosen open and time-independent physical scenario [ 43 , 44 , 45 , 46 , 47 , 48 , 49 ]. At the best of our knowledge only one paper analyzing the time evolution of concurrence versus that of quantum discord, generated by a time-dependent Hamiltonian—when the system is prepared in a convex combination of two Bell states, has been published so far [ 50 ]. The analytical solutions found for the Hamiltonian model given in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems

Ghiu

Grimaudo

Mihaescu

et al. 2020

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We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical treatment transparently unveils the physical reasons for the occurrence of such a phenomenon, relating it to the dynamical invariance of the X structure of the initial state. The quantum correlations which asymptotically emerge in the system are investigated in detail in terms of the time evolution of the fidelity of the initial Werner state.

“…The exact solution of the dynamical problem has been simplified by analyzing the different dynamically invariant subspaces emerging from the symmetry possessed by the effective Hamiltonian. This symmetry-based approach turned out to be useful to study and solve dynamical problems related to more complex interacting spin systems subjected to time-dependent fields [ 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 ]. By focusing our attention on the sub-dynamics involving the two-qubit states

and

, we brought to light the possibility of generating maximally entangled states of the two qubits.…”

Section: Conclusive Remarksmentioning

confidence: 99%

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla

Grimaudo

Messina

Sergi

et al. 2020

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In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system–environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.