Theory of Decoherence

Round Table, Hervé Zwirn C

Peter Beierle, Liyun Zhang, Herman Batelaan

A controlled decoherence environment is studied experimentally by free electron interaction with semiconducting and metallic plates. The results are compared with physical models based on decoherence theory to investigate the quantum-classical transition. The experiment is consistent with decoherence theory and rules out established Coulomb interaction models in favor of plasmonic excitation models. In contrast to previous decoherence experiments, the present experiment is sensitive to the onset of decoherence.

Klaus Hornberger

James Hefford, Matt Wilson

We find a process satisfying the axioms of hyper-decoherence which produces standard quantum theory from the theory of quantum boxes (higher-order quantum theory with the non-signalling tensor product). This hyper-decoherence map evades the no-go theorem of Lee and Selby by relaxing constraints on signalling to the past and the uniqueness of purifications. We discuss some natural opposing conclusions: that the existence of this map might be evidence of a genuine hyper-decoherence process producing causal quantum theory from its causally-indefinite higher-order theory; or that it serves as an indication that the axioms of hyper-decoherence might need careful re-consideration, especially regarding the subtle albeit central role that purity plays.

J. J. Halliwell

In the decoherent histories approach to quantum theory, sets of histories are said to be decoherent when the decoherence functional, measuring interference between pairs of histories, is exactly diagonal. In realistic situations, however, only approximate diagonality is ever achieved, raising the question of what approximate decoherence actually means and how it is related to exact decoherence. This paper explores the possibility that an exactly decoherent set of histories may be constructed from an approximate set by small distortions of the operators characterizing the histories. In particular, for the case of histories of positions and momenta, this is achieved by doubling the set of operators and then finding, among this enlarged set, new position and momentum operators that commute, and so decohere exactly, and which are ``close'' to the original operators. Two derivations are given: one in terms of the decoherence functional, the second in terms of Wigner functions. The enlarged, exactly decoherent theory has the same classical dynamics as the original one, and coincides with the so-called deterministic quantum theories of the type recently studied by 't Hooft. These results suggest that the comparison of standard and deterministic quantum theories may provide an alternative method of characterizing emergent classicality. A side product is the surprising result that histories of momenta in the quantum Brownian motion model (for the free particle in the high-temperature limit) are exactly decoherent.

Michael B. Mensky

Decoherence aiid dissipation of a quantum system occurs due to its entanglement with the environment (reservoir) . In the course of interaction of the system with the reservoir information about the system is 'recorded' in the state of the reservoir. This is why influence of the reservoir on the system (i.e. the system's decoherence and dissipation) may be accounted in the framework of quantum theory of continuous measurements. Constructing such a theory with the help of restricted path integrals (RPI) gives a model-independent theory of decoherence and dissipation. The special role of information in decoherence and dissipation is explicitly revealed by this approach. This makes it possible to apply the RPI approach for the analysis of decoherence in quantum informatic devices.