The ontological status of open quantum systems

SEBASTIAN FORTIN

Advances in Quantum Systems Research

Nova Science Publishers Inc.

Lugar: New York; Año: 2014; p. 387 - 410

In textbooks on quantum mechanics, the laws of the theory are presented as applied to closed quantum systems. Although there is no universally accepted and definitive interpretation of the formalism, certain ideas allow us to think about the concept of quantum system. The state of a closed quantum system   is represented by a density operator  , and its unitary time evolution is governed by the Schrödinger equation. The study of phenomena such as relaxation and decoherence requires the introduction of the notion of open system, that is, a quantum system that interacts with other quantum systems. In general, the subsystems of a closed system   interact with each other. The state of each one of these subsystems is represented by a reduced operator  , obtained from state   of the total system   by menas of the mathematical operation called partial trace. The reduced operator   of a subsystem allows us to compute the mean value of all its observables. For this reason, the usual practice is to conceive open subsystems as legitimate quantum systems (for example, a particle), represented by their corresponding reduced states  , whose evolution is not ruled by the Schrödinger equation. For this reason, an open quantum system can follow non-unitary evolutions, such as relaxation and decoherence [1].Decoherence is a process originally proposed to explain the diagonalization of the reduced operator [2]. The orthodox version, environment-induced decoherence (EID), only applies to open systems because, as its name implies, considers the system under study embedded in an environment that induces decoherence. According to this approach, under certain conditions the reduced state of an open system becomes diagonal, and this fact makes possible its interpretation as a classical state [3]. Thus, decoherence allows us to study the quantum-to-classical transition of a quantum system, for instance, a quantum particle.In this paper we study the properties of open systems and we discuss their ontological status. First, we compare the mathematical properties of the quantum state with those of the reduced state. Following the road opened by Bernard d´Espagnat [4], we argue that although   and   have similar mathematical structure, they cannot be interpreted in the same fashion. In a second step, we study the phenomenon of decoherence in situations where the whole closed system can be split into an open system of interest and its environment in different ways [5 - 6]. We show that the lack of a criterion to define open system and environment is a manifestation of the relative nature of decoherence, and prevents us from conceiving the open system as a physical entity of the same ontological status as that of the closed system. Finally, based on [7], we propose a formalism designed to study the phenomena of relaxation and decoherence from a closed-system perspective. Since this formalism does not appeal to reduced states, it avoids the interpretive problems mentioned above. On the basis of this work we conclude that, given the problems of interpretation derived from the notion of reduced state, the use of the notion of open systems should be avoided. According to this viewpoint, the only legitimate quantum system is the whole closed system with its unitary evolution, and the study of its dynamical properties is sufficient to describe the phenomena of decoherence and relaxation.