On Locality, Growth and Transport of Entanglement

Entanglement of a macroscopic system with a microscopic one is shown to begin by a topological property of histories in the Feynman formulation of quantum mechanics. This property can also be expressed algebraically on the Schr\"odinger equation through a convenient extension of the Hilbert space formalism. Entanglement shows then properties of growth and transport, the corresponding local and temporary character of entanglement being called here "intricacy" when it occurs. When applied to the continuous interaction of a macroscopic system with a random environment, intricacy implies a "predecoherence" effect, which can generate and transport permanently incoherence within the system. The possible relevance of these results for a theory of wave function collapse is also indicated

Predecoherence: before Decoherence and Collapse

Predecoherence, as its name indicates, is the same physical effect as decoherence, originating in the same interactions with an environment, injecting also incoherence and breaking unitarity. But whereas decoherence acts immediately after a measurement, predecoherence is acting long before. It is also a very strong effect and its main properties are established in this paper, including generation, transport, damping, and stationary level. A mechanism for objectification, or wave function collapse, is also proposed as consisting in a perturbation by predecoherence of the intricacy between a measuring system and a measured one. The theory is made explicit on a special example and the quantitative results are found sensible.Comment: 24 page

Decoherence and wave function collapse

The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wave function collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character of quantum mechanics

Quelques remarques à propos du problème de la réalité

Un certain temps s’est écoulé depuis l’agréable rencontre qui s’est tenue à Caen, si bien que les idées émises alors par certains d’entre nous ont pu évoluer ou perdre de leur actualité. En ce qui me concerne, il se trouve que la partie essentielle de ma propre contribution d’alors a été publiée dans l’intervalle et, en outre, diverses réflexions m’ont conduit depuis à considérer la question de la réalité sous un nouveau jour. Certaines de ces i..

Mesoscopic superpositions of vibronic collective states of N trapped ions

We propose a scalable procedure to generate entangled superpositions of motional coherent states and electronic states in N trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies of decoherence.Comment: Final version, as published in Physical Review Letters. See also further developments and applications in quant-ph/020207

Decoherence, irreversibility and the selection by decoherence of quantum states with definite probabilities

The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation. Two distinct cases of decoherence are then found: (i) A ``degenerate'' case (already encountered with solvable models) where decoherence amounts essentially to approximate diagonalization; (ii) A general case where the einselected states are essentially classical. They are mixed states. Their density operators are proportional to microlocal projection operators (or ``quasi projectors'') which were previously introduced in the quantum expression of classical properties. It is found at various places that the main limitation in our understanding of decoherence is the lack of a systematic method for constructing collective observables.Comment: 54 page