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arXiv:1009.3659 · Physica Scripta

Disentanglement and decoherence without dissipation at non-zero temperatures

G. W. Ford, Robert F. O’Connell

Published Aug 18, 2010• 5 citations
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Abstract

Decoherence is well understood, in contrast to disentanglement. According to common lore, irreversible coupling to a dissipative environment is the mechanism for loss of entanglement. Here, we show that, on the contrary, disentanglement can in fact occur at large enough temperatures $T$ even for vanishingly small dissipation (as we have shown previously for decoherence). However, whereas the effect of $T$ on decoherence increases exponentially with time, the effect of $T$ on disentanglement is constant for all times, reflecting a fundamental difference between the two phenomena. Also, the possibility of disentanglement at a particular $T$ increases with decreasing initial entanglement.

DOI
10.1088/0031-8949/82/03/038112

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Decoherence is well understood, in contrast to disentanglement. According to common lore, irreversible coupling to a dissipative environment is the mechanism for loss of entanglement. Here, we show that, on the contrary, disentanglement can in fact occur at large enough temperatures TTT even for vanishingly small dissipation (as we have shown previously for decoherence). However, whereas the effect of TTT on decoherence increases exponentially with time, the effect of TTT on disentanglement is constant for all times, reflecting a fundamental difference between the two phenomena. Also, the possibility of disentanglement at a particular TTT increases with decreasing initial entanglement.
The prototypical Schr\\"{o}dinger cat state, i.e., an initial state corresponding to two widely separated Gaussian wave packets, is considered. The decoherence time is calculated solely within the framework of elementary quantum mechanics and equilibrium statistical mechanics. This is at variance with common lore that irreversible coupling to a dissipative environment is the mechanism of decoherence. Here, we show that, on the contrary, decoherence can in fact occur at high temperature even for vanishingly small dissipation.
Most discussions of decoherence in the literature consider the high temperature regime but it is also known that, in the presence of dissipation, decoherence can occur even at zero temperature. Whereas most previous investigations all assumed initial decoupling of the quantum system and bath, we consider that the system and environment are entangled at all times. Here, we discuss decoherence for a free particle in an initial Schrödinger cat state. Memory effects are incorporated by use of the single relaxation time model.
We study a dynamic process of disentanglement by considering the time evolution of bound entanglement for a quantum open system, two qutrits coupling to a common environment. Here, the initial quantum correlations of the two qutrits are characterized by the bound entanglement. In order to show the universality of the role of environment on bound entanglement, both bosonic and spin environments are considered. We found that the bound entanglement displays collapses and revivals, and it can be stable against small temperature and time change. The thermal fluctuation effects on bound entanglement are also considered.
Decoherence and disentanglement are phenomena central to quantum mechanics. Here, we consider the relative rates of decoherence and disentanglement in two‐qubit, three‐qubit, and two‐qutrit systems when subject to pure dephasing noise alone, and a very recent result for d×d systems. Of particular interest is the specific counterintuitive effect related to the nonadditivity of such weak noises, known as Entanglement Sudden Death (ESD), in which the entanglement of a composite quantum system goes abruptly to zero in finite time, coherence only exponentially decaying. We discuss these results in the context of the foundations of quantum mechanics.
This thesis investigates the time evolution of the entangled B0-B0-bar system by calculating the effects of disentanglement and decoherence. The disentanglement is implemented by inserting a factor ζ, which can be constant or time-dependent. This phenomenon changes the asymmetry of B0-B0-bar mixing by a phase shift and an amplitude decrease. This is similar to mistag in flavour tagging, so the consideration of this effect is needed to decrease systematic errors of TDCPV measurements. Decoherence can arise from the interaction of one particle with the environment, which results in a time-dependent damping of the oscillation amplitude. The different time propagations of |BH⟩ and |BL⟩, which are dependent on the mass difference, could be a reason for decoherence. The interaction of quantum black holes could also enhance the effect. Both disentanglement and decoherence are combined to form a detailed description of the time evolution of an entangled system. Furthermore, this work provides another approach of implementing disentanglement by using density matrices. Now, the system can be formulated as a combination of the entangled and the disentangled case, where ζ is the fraction. Moreover, it is shown that the CHSH inequality is violated, even when the oscillations are completely disentangled, because the B0-mesons do not oscillate fast enough due to their small mass difference and short mean lifetime.