A Bohmian view on quantum decoherence

– The implications of quantum decoherence within the context of Bohmian mechanics are analyzed. By using the double–slit experiment as an example, we show that decoherence is not a sufficient mechanism to obtain the classical limit. Our results show that although decoherence produces an intensity pattern identical to the classical one (without interference), there still remain non–local (quantum) correlations. Bohmian mechanics shows that the individual motion of quantum particles presents such correlations even in the case of total decoherence. Introduction. – Although different alternatives have been proposed to account for the problem of how quantum systems become classical [1], the theory of decoherence seems to be the most widely accepted [2,3]. In this context, decoherence is understood as the “irreversible emergence of classical properties through interaction with the environment” [4], leading to the suppression of quantum interference. This interaction may take place via scattering processes [5], since, when taking place in a large number, they produce an exponential damping of the non–diagonal elements of the density matrix, which are responsible for interferences. However, Omnès [1] doubts that decoherence, in spite of its importance, may be the final answer to the problem of the loss of coherence in quantum mechanics. Although the reduced density operator becomes diagonal, the full density operator ρ(t) still represents a pure state with a permanent superposition, as long as the system remains isolated. Thus, this author considers the question about the possibility “to perform a very refined measurement upon the environment, revealing the existence of quantum interferences”. Although Zurek [6] suggests a pragmatic negative answer to this question, since such measurements are not possible in practice, Omnès’ opinion is that it should be possible to go further. This last question has an important practical interest in quantum information theory, in particular, in quantum computation [7]. The mechanisms used to perform quantum operations rely on chains of atoms in a coherent superposition. To achieve high efficiency, long chains of atoms must be kept in such states for certain time, thus allowing more sophisticated computations as the chain length increases. However, decoherence effects increase also rapidly with the chain lengh [8]. (∗) E-mail: [email protected] (∗∗) E-mail: [email protected]