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Acta Physica Sinica

On the validity of factorization law for the entanglement evolution of two qubits

Huo Ya-Jing, Li Jun-Gang

Published Jan 1, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.61.210304

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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.
The entanglement evolution of two qubits under local, single-, and two-sided noisy channels is investigated. It is found that for all pure initial states, the entanglement under a one-sided noisy channel is completely determined by the maximal trace distance which is the main element to construct the measure of non-Markovianity. For the two-sided noisy channel case, when the qubits are initially prepared in a general class of states, either pure or mixed, the entanglement can be expressed as the product of the initial entanglement and the channels' action on the maximally entangled state.
Here is analyzed the dynamics of two-qubit entanglement, when the two qubits are initially in a mixed extended Werner-like state and each of them is in a zero temperature non-Markovian environment. The dependence of entanglement dynamics on the purity and degree of entanglement of the initial states and on the amount of non-Markovianity is also given. This extends the previous work about non-Markovian effects on the two-qubit entanglement dynamics for initial Bell-like states [Bellomo et al., Phys. Rev. Lett. 99, 160502 (2007)]. The effect on the two-qubit entanglement dynamics of nonzero temperature in Markovian environments is finally studied.
We explore how entanglement of a bipartite system evolves when one subsystem undergoes the action of an arbitrary noisy channel. It is found that the dynamics of entanglement of such system is determined by the channel's action on the maximally entangled state, which includes as a special case the results for two-qubit systems [Konrad et al., Nat. Phys. 4, 99 (2008)]. In particular, for multiqubit or qubit-qudit systems, we get a general factorization law for the evolution equation of entanglement, with one qubit being subject to a noisy channel.
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 entanglement evolution of a pair of two-level systems is studied in this paper. The two systems without mutual interaction are independently coupled to different two-band non-Markovian environments. By comparing our results to others in the literature, we find that taking one of the Bell states as the initial state, certain non-Markovian effect protects the entanglement in short time scale, while on long time scale it leads to the entanglement sudden death (ESD), which never occurs for this initial state in the Markovian case. Finally, by analyzing the parameters in our model, a relation between disentanglement and decoherence is established and discussed.
As a quantum resource, quantum coherence plays an important role in modern physics. Many coherence measures and their relations with entanglement have been proposed, and the dynamics of entanglement has been experimentally studied. However, the knowledge of general results for coherence dynamics in open systems is limited. Here we propose a coherence factorization law that describes the evolution of coherence passing through any noisy channels characterized by genuinely incoherent operations. We use photons to implement the quantum operations and experimentally verify the law for qubits and qutrits. Our work is a step toward understanding of the evolution of coherence when the system interacts with the environment, and will boost the study of more general laws of coherence.