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Physics Letters A

Factorization law for entanglement evolution of two qubits in non-Markovian pure dephasing channels

Jungang Li, Jian Zou, Bin Shao

Published May 7, 2011• 10 citations
Publisher
DOI
10.1016/j.physleta.2011.04.053

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The validity of factorization law for the entanglement evolution of two qubits coupled to two independent non-Markovian channels is investigated. It is found that for some initial states, such as the Bell state and the maximally entangled mixed state, the entanglement can be characterized by the factorized entanglement when the effects of the channels are weak. For the general initial states, the factorized entanglement provides us with a good approximation to characterize the entanglement dynamics when the entanglement is large.
Gravitational redshift can cause the distortion of photon wave packets; thus, the non-Markovian speedup evolution of a photon system must be controlled by considering gravitational redshift. We analyze the non-Markovian speedup dynamics of a photon system in the amplitude-damping channel or pure-dephasing channel under the effect of gravitational redshift, which is modelled as a beam-splitter operation. We show that the gravitational redshift weakens the non-Markovian dynamical behavior in both channels. For the amplitude-damping channel, the gravitational redshift promotes further speedup evolution of a photon system when the initial coherence of the system is nonzero. A stronger gravitational redshift and larger initial coherence make improving the evolution speed of the photon system easier. For the pure-dephasing channel, the non-Markovian dynamical behavior decreases owing to the gravitational redshift; however, the evolution speed of the photon is not influenced by the gravitational redshift.
We evaluate the non-Markovian finite-temperature two-time correlation functions (CF's) of system operators of a pure-dephasing spin-boson model in two different ways, one by the direct exact operator technique and the other by the recently derived evolution equations, valid to second order in the system-environment interaction Hamiltonian. This pure-dephasing spin-boson model that is exactly solvable has been extensively studied as a simple decoherence model. However, its exact non-Markovian finite-temperature two-time system operator CF's, to our knowledge, have not been presented in the literature. This may be mainly due to the fact, illustrated in this article, that in contrast to the Markovian case, the time evolution of the reduced density matrix of the system (or the reduced quantum master equation) alone is not sufficient to calculate the two-time system operator CF's of non-Markovian open systems. The two-time CF's obtained using the recently derived evolution equations in the weak system-environment coupling case for this non-Markovian pure-dephasing model happen to be the same as those obtained from the exact evaluation. However, these results significantly differ from the non-Markovian two-time CF's obtained by wrongly directly applying the quantum regression theorem (QRT), a useful procedure to calculate the two-time CF's for weak-coupling Markovian open systems. This demonstrates clearly that the recently derived evolution equations generalize correctly the QRT to non-Markovian finite-temperature cases. It is believed that these evolution equations will have applications in many different branches of physics.