The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. For this purpose a general and analytically solvable decoherence model is presented which does not involve any weak-coupling or Markovian assumption. It is shown that two fundamentally different classes of entangled states can be distinguished and that they can be influenced significantly by two important environmental properties, namely, its initially prepared state and its size. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.
The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. For this purpose a general and analytically solvable decoherence model is presented which does not involve any weak-coupling or Markovian assumption. It is shown that two fundamentally different classes of entangled states can be distinguished and that they can be influenced significantly by two important environmental properties, namely, its initially prepared state and its size. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.
We study the robustness and fragility of entanglement of open quantum systems in some exactly solvable models in which the decoherence is caused by a pure dephasing process. In particular, for the toy models presented in this paper, we identify two different time scales, one is responsible for local dephasing, while the other is for entanglement decay. For a class of fragile entangled states defined in this paper, we find that the entanglement of two qubits, as measured by concurrence, decays faster asymptotically than the quantum dephasing of an individual qubit.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.
The destruction of quantum interference, decoherence, and the destruction of entanglement both appear to occur under the same circumstances. To address the connection between these two phenomena, we consider the evolution of arbitrary initial states of a two-particle system under open system dynamics described by a class of master equations which produce decoherence of each particle. We show that all initial states become separable after a finite time, and we produce the explicit form of the separated state. The result extends and amplifies an earlier result of Di\'osi. We illustrate the general result by considering the case in which the initial state is an Einstein-Podolsky-Rosen state (in which both the positions and momenta of a particle pair are perfectly correlated). This example clearly illustrates how the spreading out in phase space produced by the environment leads to certain disentanglement conditions becoming satisfied.
We show that the entanglement evolution of an open quantum system is the same for the vast majority of initial pure states, in the limit of large Hilbert space dimensions. The analytical results are illustrated by a numerical study of the evolution of negativity for many-qubit systems undergoing a local decoherence process. In the limit of many subsystems, the arising mixed state entanglement between one subsystem and the rest grows more robust, whereas for two equally sized partitions it becomes more fragile.
Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.
Entanglement is a fundamental concept in quantum mechanics. In this review, we study various aspects of coherence and entanglement, illustrated by several examples. We relate the concepts of loss of coherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including cases of both independent and common baths. Finally, we relate decoherence and disentanglement, by focusing on the sudden death of the entanglement and the dependence of the death time with the distance of our initial condition from the decoherence-free subspace. In particular, we study the sudden death of the entanglement in a two-atom system with a common reservoir.