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arXiv:1705.09812 · Physical Review A

Emergence of entanglement with temperature and time in factorization-surface states

Titas Chanda, Tamoghna Das, Debasis Sadhukhan, Amit Kumar Pal, Aditi Sen, Ujjwal Sen

Published Jan 16, 2018• 7 citations
arXivHTMLPDF

Abstract

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting with the system through that spin-pair via a repetitive quantum interaction.

DOI
10.1103/physreva.97.012316

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We consider an infinite one-dimensional anisotropic XY\mathit{XY}XY spin chain with a nearest-neighbor time-dependent Heisenberg coupling J(t)J(t)J(t) between the spins in presence of a time-dependent magnetic field h(t)h(t)h(t). We discuss a general solution for the system and present an exact solution for particular choice of JJJ and hhh of practical interest. We investigate the dynamics of entanglement for different degrees of anisotropy of the system and at both zero and finite temperatures. We find that the time evolution of entanglement in the system shows nonergodic and critical behavior at zero and finite temperatures and different degrees of anisotropy. The asymptotic behavior of entanglement at the infinite time limit at zero temperature and constant JJJ and hhh depends only the parameter $\ensuremath{\lambda}=J/h$ rather than the individual values of JJJ and hhh for all degrees of anisotropy but changes for nonzero temperature. Furthermore, the asymptotic behavior is very sensitive to the initial values of JJJ and hhh and for particular choices we may create finite asymptotic entanglement regardless of the final values of JJJ and hhh. The persistence of quantum effects in the system as it evolves and as the temperature is raised is studied by monitoring the entanglement. We find that the quantum effects dominate within certain regions of the kT\mathit{kT}kT-$\ensuremath{\lambda}$ space that vary significantly depending on the degree of the anisotropy of the system. Particularly, the quantum effects in the Ising model case persist in the vicinity of both its critical phase transition point and zero temperature as it evolves in time. Moreover, the interplay between the different system parameters to tune and control the entanglement evolution is explored.
Quantum correlations (including entanglement and quantum discord) of two qubits symmetrically coupled to the surrounding XY spin chain in the presence of a transverse magnetic field are studied. We investigate the dynamic evolution of the quantum correlations of the two qubits when the surrounding spin chain is in the thermal equilibrium state. Numerical results show that the thermal effects can accelerate the decay process of the quantum correlations if the initial state of the composite system is not in the decoherence free space. When the temperature is high enough, the quantum phase transition driven by the external magnetic field completely disappear.
We describe the evolution of the quantum entanglement of an open system consisting of two bosonic modes interacting with a common thermal environment, described by two different models. The initial state of the system is taken of Gaussian form. In the case of a thermal bath, characterized by temperature and dissipation constant which correspond to an asymptotic Gibbs state of the system, we show that for a zero temperature of the thermal bath an initial entangled Gaussian state remains entangled for all finite times. For an entangled initial squeezed thermal state, the phenomenon of entanglement sudden death takes place and we calculate the survival time of entanglement. For the second model of the environment, corresponding to a non-Gibbs asymptotic state, we study the possibility of generating entanglement. We show that the generation of the entanglement between two uncoupled bosonic modes is possible only for definite values of the temperature and dissipation constant, which characterize the thermal environment.
The challenge of harnessing entanglement during the non-equilibrium dynamics of open quantum systems, especially at high temperatures, is highly prominent within recent scientific researches. Due to the ongoing trend of miniaturization of quantum devices that exploit quantum correlations, proposing novel schemes to overcome this challenge is itself a crucial task within current quantum technological research. We contribute to this research by proposing a new scheme to control entanglement dynamics of a non-equilibrium two-qubit Heisenberg XXZ spin chain model in an external magnetic field. The design of the scheme is based on a coupling asymmetry in the model induced by the asymmetrical connection of qubits to two independent thermal reservoirs. While in the absence of the coupling asymmetry, non-equilibrium effects generally suppress the dynamical generation of thermal entanglement, making entanglement production impossible at high mean temperatures of reservoirs, it is shown that this asymmetry in the coupling potentially enables us to generate a maximal non-equilibrium entanglement even in the high mean temperature regime. We show that the coupling asymmetry can also lead to a complete protection of the maximum initial entanglement between the qubits at high mean temperatures of the reservoirs thanks to the non-equilibrium conditions. Depending on the initial state of the two qubits, this can be achieved either by accessing a coherence-free subspace or by fully reviving the initial qubit-qubit entanglement. Furthermore, we investigate the quantum heat transport of the chain, and find that by turning on the asymmetry in the qubit-reservoir coupling, although the chain loses its initial thermal rectification property over time, it regains this property and maintain it until the non-equilibrium steady state is reached. Our results show that, at higher temperature gradients, the chain leverages the steady-state entanglement to completely block the heat released from the hot reservoir. Our findings can be significant for heat management in quantum computing devices such as solid-state thermal circuits.
We study and compare the persistence of bipartite entanglement (BE) and multipartite entanglement (ME) in one-dimensional and two-dimensional spin XY models in an external transverse magnetic field under the effect of thermal excitations. We compare the threshold temperature at which the entanglement vanishes in both types of entanglement. We use the entanglement of formation as a measure of the BE and the geometric measure to evaluate the ME of the system. We have found that in both dimensions in the anisotropic and partially anisotropic spin systems at zero temperatures, all types of entanglement decay as the magnetic field increases but are sustained with very small magnitudes at high field values. Also we found that for the same systems, the threshold temperatures of the nearest neighbour (nn) BEs are higher than both of the next-to-nearest neighbour BEs and MEs and the three of them increase monotonically with the magnetic field strength. Thus, as the temperature increases, the ME and the far parts BE of the system become more fragile to thermal excitations compared to the nn BE. For the isotropic system, all types of entanglement and threshold temperatures vanish at the same exact small value of the magnetic field. We emphasise the major role played by both the properties of the ground state of the system and the energy gap in controlling the characteristics of the entanglement and threshold temperatures. In addition, we have shown how an inserted magnetic impurity can be used to preserve all types of entanglement and enhance their threshold temperatures. Furthermore, we found that the quantum effects in the spin systems can be maintained at high temperatures, as the different types of entanglements in the spin lattices are sustained at high temperatures by applying sufficiently high magnetic fields.
We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.