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arXiv:2109.03965

Dynamics of tripartite correlations for three qubits in independent thermal reservoirs

Sourabh Magare, Abhinash Kumar Roy, Prasanta Kumar Panigrahi

Published Sep 7, 2021• 0 citations
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Abstract

We investigate the dynamical evolution of multipartite entanglement in tripartite systems with three qubits present in independent thermal reservoirs, modelled as infinite set of quantum harmonic oscillators. We show that the presence of temperature gradient between reservoirs play a significant role in robustness of multipartite correlation against environmental decoherence. Considering a bilinear form of interaction Hamiltonian, an exact expression for time evolved density matrix is presented. Interestingly, it is observed that the preservation duration of genuine multipartite concurrence for GHZ class Werner state increases as the temperature gradient between reservoirs are increased. However, this increase is non-linear and the preservation duration is shown to saturate for large temperature gradients. It is also observed that, for large temperature gradient, there are multiple intervals in which coherence and consequently the tripartite negativity shows robustness (freezing of correlation) against the environmental decoherence for W class Werner states. For the common temperature case, we show that the genuine multipartite concurrence for the GHZ class Werner state decays irreversibly, and the state experiences correlation sudden death, with a rate dependent on spectral density of the reservoirs under consideration. For the Ohmic reservoirs at low temperature, we observe that the state retains initial multipartite correlation upto a characteristic time and then sharply decays to zero with a correlation sudden death. We further investigate the dynamics of tripartite negativity and $l_{1}$ norm of coherence in the W class Werner states, and show irreversible degradation in these correlations.

DOI
10.48550/arxiv.2109.03965

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We investigate the dynamical evolution of multipartite entanglement in tripartite systems with three qubits present in independent thermal reservoirs, modelled as infinite set of quantum harmonic oscillators. We show that the presence of temperature gradient between reservoirs play a significant role in robustness of multipartite correlation against environmental decoherence. Considering a bilinear form of interaction Hamiltonian, an exact expression for time evolved density matrix is presented. Interestingly, it is observed that the preservation duration of genuine multipartite concurrence for GHZ class Werner state increases as the temperature gradient between reservoirs are increased. However, this increase is non-linear and the preservation duration is shown to saturate for large temperature gradients. It is also observed that, for large temperature gradient, there are multiple intervals in which coherence and consequently the tripartite negativity shows robustness (freezing of correlation) against the environmental decoherence for W class Werner states. For the common temperature case, we show that the genuine multipartite concurrence for the GHZ class Werner state decays irreversibly, and the state experiences correlation sudden death, with a rate dependent on spectral density of the reservoirs under consideration. For the Ohmic reservoirs at low temperature, we observe that the state retains initial multipartite correlation upto a characteristic time and then sharply decays to zero with a correlation sudden death. We further investigate the dynamics of tripartite negativity and l1l_{1}l1​ norm of coherence in the W class Werner states, and show irreversible degradation in these correlations.
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.
Accurate temperature measurement at the quantum scale is becoming increasingly important for emerging quantum technologies, motivating the development of quantum thermometry based on quantum resources. In this work, we investigate how finite environmental temperature influences the coherence dynamics of multipartite quantum systems and examine whether quantum coherence can serve as a temperature sensitive observable. We consider a tripartite spin-boson model interacting with finite temperature dephasing environments under two physically distinct reservoir configurations, namely local and common environments. The dynamics of representative tripartite pure and mixed states are quantified using the relative entropy of coherence. Our results show that local dephasing produces a universal monotonic decay of coherence, with increasing temperature accelerating decoherence for all states. In contrast, common dephasing generates a markedly state dependent thermal response. Under common dephasing, the ∣GHZ⟩\vert GHZ \rangle∣GHZ⟩ and ∣Star⟩\vert Star\rangle∣Star⟩ states undergo complete coherence loss, the ∣W⟩\vert W\rangle∣W⟩ state exhibits temperature independent stationary coherence, and the ∣WW‾⟩\vert W\overline{W}\rangle∣WW⟩ state retains finite residual coherence at long times. Similar state dependent behaviour is also observed for mixed states. These results demonstrate that the thermal susceptibility of quantum coherence is governed jointly by the environmental configuration and the internal architecture of the multipartite quantum state. Furthermore, we establish a direct coherence temperature correspondence through representative thermometry tables, providing a \textit{proof-of-principle} foundation for coherence based quantum thermometry.
Abstract We address the time evolution of quantum correlations (QCs) such as entanglement, purity, and coherence for a model of two non-interacting qubits initially prepared as a maximally entangled bipartite state. We contrast the comparative potential of the classical fields to preserve these QCs in the noisy and noiseless realms. We also disclose the characteristic dynamical behavior of the QCs of the two-qubit state under the static noise effects originating from the common and different configuration models. We show that there is a direct connection between the fluctuations allowed by an environment and the preservation of QCs. Due to the static noise dephasing effects, the QCs are suppressed, resulting in the separability of the two-qubit entangled state after a finite duration. For bipartite QCs preservation, we show that the common configuration is more resourceful than the different configuration. Furthermore, this protection of the QCs under static noise for large intervals is entirely attributable to the existence of the entanglement sudden death and birth phenomenon. Most importantly, we found the bipartite QCs less fragile than the tripartite ones in comparison under the static noise. In addition, we find the concurrence measure to show more evident revivals of entanglement in comparison.
A meaningful description of the low-energy dynamics of multipartite entanglement is provided\nfor harmonic oscillator systems in general dissipative scenarios. Without doing any\ncentral approximation, this mainly relies on a set of reasonable physical statements on the\nenvironment and system-environment interaction consistent with a linear analysis of the\nopen-system dynamics.\nWe rst investigate the inseparability properties of arbitrary entangled states, which\ngenerally entails an optimization procedure of certain functional de ned in the in nitedimensional\nHilbert space of continuous-variable systems. Using a Gaussian-like assumption\nanalogous to that used in the derivation of Gaussian entanglement of formation, we\nderive a computational-e cient form of such functional which considerable simpli es the\noptimization task. This consists on a hierarchy of separability criteria that permit in a\nuni ed way to characterize k-partite entanglement of broad classes of Gaussian and non-\nGaussian states. The strength of the criteria is proven by showing that they satisfactorily\nreproduce previous results from the theory of entanglement, like PPT criterion applied to\narbitrary two-mode and pure three-mode Gaussian states.\nThe separability criteria allow to monitor the transient evolution of multipartite entanglement\nunder the environmental in\nuence, this permitted to show that non-Gaussian\nentanglement may be as robust against harmful dissipative e ects and thermal noise as\nGaussian one. We devote special attention to the stationary properties of tripartite entanglement\nwhen the system oscillators are in contact with either a common environment\nor independent environments at initial di erent temperatures. For the former dissipative\nscheme, it is shown that the environment mediates an e ective many-party interaction with\na spatial long-range feature between system oscillators, which is able to generate tripartite\nentanglement whereas two-mode entanglement is degraded. Regarding the second scheme,\nit is illustrated that thermal non-equilibrium conditions result in a rich variety of quantum\ncorrelations, however a temperature gradient eventually destroys the entanglement shared\nby the system oscillators as a consequence of the growth of thermal noise. Finally, the\nstationary entanglement and energy current across a nite harmonic chain are studied in\ndetail by doing an extensive numerical analysis of both phenomena for a broad range of the\nparameters (i.e., temperatures, oscillator frequencies, and oscillator coupling strengths).\nOur numerical ndings are discussed in terms of the derived energy current expressions,\nthese show an explicit dependence on the two-time correlation functions (between oscillator\noperators) which carry quantum correlations.
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.