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Chapman & Hall/CRC applied mathematics and nonlinear science series

Analysis of Quantum Evolutions; Entanglement, Entanglement Measures and Dynamics

Published Aug 3, 2007• 0 citations
Publisher
DOI
10.1201/9781584888833.ch8

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Entanglement of quantum systems refers to the situation where two or more systems interact and the state of the whole system cannot be seen as a superposition of states of the single systems. This chapter is devoted to the definition of entanglement both for pure states and mixed states. It also discusses methods to detect entanglement. The chapter is devoted to the study of the dynamics of entanglement. It is also devoted to the problem of local equivalence between states, i.e., how to determine when, given two states, it is possible to evolve from one to the other by transformations which act on systems separately.
We investigate the entanglement dynamics of three-qubit states in a quantum-critical environment, which is an Ising model in a transverse field. By using negativity as entanglement measure, we find that the entanglement evolution depends not only on the system-environment couplings and the size of degrees of freedom of environment but also on the strength of transverse field and the symmetry of quantum states of concern. In particular, for the cases under study, our results imply that the entanglement decay can be enhanced by the quantum phase transition of the environment under weak coupling. Our analysis implies that the entanglement of any three-qubit quantum state will be completely destroyed by the decoherence under certain conditions, that we detail below.
Information that is stored in quantum-mechanical systems can be easily lost because of the interaction with the environment in a process known as decoherence. Possible physical implementations of many processes in quantum information theory involve systems of identical particles, whence comprehension of the dynamics of entanglement induced by decoherence processes in identical-particle open systems becomes relevant. Here we study the effects and concomitant entanglement evolution arising from the interaction between a system of two identical fermions and the environment for two paradigmatic quantum channels. Entanglement measures are introduced to quantify the entanglement between the different parties, and a study of the dynamics of entanglement for some particular examples is carried out. Our analysis, which includes also the evolution of an entanglement indicator based on an entropic criteria, offers insights into the dynamics of entanglement in open systems of identical particles, involving the emergence of multipartite genuine entanglement. The results improve our understanding of the phenomenon of decoherence and will provide strategies to control it.