Abstract
We investigate the dynamical evolution of genuine multipartite correlations for N-qubits in a common reservoir considering a non-dissipative qubits-reservoir model. We derive an exact expression for the time-evolved density matrix by modeling the reservoir as a set of infinite harmonic oscillators with a bilinear form of interaction Hamiltonian. Interestingly, we find that the choice of two-level systems corresponding to an initially correlated multipartite state plays a significant role in potential robustness against environmental decoherence. In particular, the generalized W-class Werner state shows robustness against the decoherence for an equivalent set of qubits, whereas a certain generalized GHZ-class Werner state shows robustness for inequivalent sets of qubits. It is shown that the genuine multipartite concurrence (GMC), a measure of multipartite entanglement of an initially correlated multipartite state, experiences an irreversible decay of correlations in the presence of a thermal reservoir. For the GHZ-class Werner state, the region of mixing parameters for which there exists GMC, shrinks with time and with increase in the temperature of the thermal reservoir. Furthermore, we study the dynamical evolution of the relative entropy of coherence and von-Neumann entropy for the W-class Werner state.
Highlights
Entanglement arising from the superposition principle and tensorial structure of Hilbert spaces is a striking feature of multiparty quantum systems [1]
We found an exact expression for a time-evolved density matrix for an N-qubit system in a common heat bath through a thermal reservoir modeled as an infinite quantum harmonic oscillator and a bilinear non-dissipative interaction Hamiltonian
We studied the dynamics of the underlying multipartite correlation for various Nqubit systems
Summary
Entanglement arising from the superposition principle and tensorial structure of Hilbert spaces is a striking feature of multiparty quantum systems [1]. A closed expression exists only for X-type states, wherein only the diagonal and anti-diagonal elements are non-zero Another measure widely studied for mixed three-qubit states is the tripartite negativity, which is defined through the geometric mean of negativity corresponding to the three bipartitions [23]. Dynamics of a more general bipartite correlation, namely quantum discord for two initially correlated qubits in two different reservoirs, was studied for ohmic reservoirs [38], and it was shown that the preservation duration gets longer, the lower the temperature of the environment, the weaker the environmental coupling, and the larger the temperature difference between the reservoirs.
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