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Journal of Physics A Mathematical and Theoretical

Entanglement persistence in contact with the environment: exact results

Jerzy Dajka, Marcin Mierzejewski, J. Łuczka

Published Aug 29, 2007• 20 citations
Publisher

Abstract

The evolution of quantum entanglement of a pair of non-interacting qubits is studied for the case where one of them is non-dissipatively but dephasingly coupled to the environment. The reduced non-Markovian dynamics of the qubits is exact for an arbitrary strength of coupling to the environment and the arbitrary frequency spectrum of environment fluctuations. While for the subohmic and ohmic environments the entanglement diminishes, for the superohmic zero-temperature environment it survives for a long time.

DOI
10.1088/1751-8113/40/37/f01

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The evolution of quantum entanglement of a pair of non-interacting qubits is studied for the case where one of them is non-dissipatively but dephasingly coupled to the environment. The reduced non-Markovian dynamics of the qubits is exact for an arbitrary strength of coupling to the environment and the arbitrary frequency spectrum of environment fluctuations. While for the subohmic and ohmic environments the entanglement diminishes, for the superohmic zero-temperature environment it survives for a long time.
Two noninteracting qubits, initially prepared in an entangled state, are coupled to their own independent environments and evolve under their influence. The reduced non-Markovian dynamics of two qubits is exact for arbitrary model parameters. Necessary and sufficient conditions for nonvanishing entanglement are formulated for both zero and nonzero temperatures and arbitrary time. It is shown that (i) entanglement dynamics can effectively be controlled by a finite quantum system coupled to one of the qubits and (ii) dynamical symmetry of the controlling quantum system can influence significantly entanglement of the qubits and results in its nonmonotonic decay.
The exact reduced dynamics for two independent qudits dephasingly coupled to a common zero-temperature, super-Ohmic, bosonic environment is studied. It is shown that the qudit-qudit subsystem initially prepared in a separable state evolves into an entangled state. Details of the entanglement origination depend on both the coupling strength and the spectral properties of the environment as well as on the dimension of the qudit; the environment-induced entanglement can survive in the long-time limit. The entanglement dynamics of initially maximally entangled qudit-qudit states is analyzed for two examples: the qubit-qubit and qutrit-qutrit systems. The theory is applied to negative partial transposition entangled states of a two-qutrit system, which are shown to be distillable (for the assumed initial state) for arbitrary environment parameters.
environment on the entanglement dynamics in non-Markov process. Our results show that the entanglement degree is strongly related with the initial quantum state and the coupling between the qubits and the environment. The interaction between the qubits and the environment suppresses the decay of the entanglement. The sudden death of entanglement (ESD) can be prevented only by using and controlling targeted the interaction model between the different qubits and the environment. We also find the dissipation phenomenon always exists when the qubits system is initially in the maximally entangled mixed states.
Two non-directly interacting qubits with equal frequencies can become entangled via a Markovian, dissipative dynamics through the action of a weakly coupled Ohmic heat bath. In the standard weak-coupling limit derivation, this purely dissipative effect disappears if the frequencies are different because of the “ergodic average” used by this approach. However, there are physical situations where this technique is too rough to capture all the relevant aspects of the dissipative dynamics. In these cases, in order to better describe the physical behavior of the open system, it is necessary to go beyond the “ergodic average”. We show that, in this more refined framework, the entanglement capability of the environment persists also in the case of different frequencies.
One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state.