Parallel decoherence in composite quantum systems

Abstract

For the standard Quantum Brownian Motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard, one Brownian particle, we show there is at least another one system undergoing the dynamics described by the QBM effect. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. A generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context. PACS 03.65.Yz Decoherence; open systems; quantum statistical methods PACS 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) PACS 03.65.Ta Foundations of quantum mechanics; measurement theory one and the same composite system of the QBM model that cannot be obtained from each other via the "coarse graining" [6] operation.The LCTs is a universal physical method. Already the unitary evolution regroups or separates the constituent subsystems thus locally changing a structure of a composite system. In quantum decoherence, the LCTs are sometimes used to ease the calculation [5], while (kinematically) regrouping or decomposing the subsystems may shed some new light on the mechanism of decoherence [7,8]. A change in the environmental degrees of freedom reveals some subtleties such as the "system-size" dependence of decoherence [5,9] and can help in distinguishing the robust (the preferred "pointer basis" [4, 5, 10, 11]) states for the open system [12,13,14]. However, these models and considerations refer to the local structures that share the degrees of freedom or can be reduced to each other. This makes the structures considered mutually dynamically coupled or dependent, which is not our objective.Paradigmatic for our considerations is the Hydrogen Atom (HA) model. The quantum theory of the hydrogen atom relies on the transformations of the electron's (e) and the proton's (p) degrees of freedom to introduce the atom center of mass (CM) and the "relative position (R)" degrees of freedom. Due to the absence of the coupling between CM and R, one obtains the variables separation and the exact solution of the atomic internal energy and eigenstates. The two structures of HA, e + p and CM + R, are mutually both irreducible and global likewise those of the QBM setup we discuss below.In Section 2, we derive our main result on the parallel decoherence: at variance with the standard wisdom, we point out that a composite quantum system can be described by (may host) the different, simultaneously existing and mutually independent quasi-classical (global) structures. In Section 3 we generalize our considerations and we emphasize that the "parallel decoherence" launches a new task in the foundations of the decoherence theory. In general, this task can be formidable yet possibly of a wider scientific interest. Section 4 is Discussion, where we emphasize: as long...

Interpretation neutrality in the classical domain of quantum theory

“…An operatorÔ is positive if it is self-adjoint and Ψ|Ô|Ψ ≥ 0 for every |Ψ ∈ H. Note that every PVM is also a POVM. 16…”

A Top-down versus a Bottom-up Hidden-variables Description of the Stern–Gerlach Experiment

“…[15]-that here will not be considered. The secondary role of "quantum subsystems", which lack independent individuality, is exhibited by the so-called "parallel occurrence of decoherence" on the purely formal level in the context of the standard environment-induced decoherence theory [16]. Simultaneous unfolding of the mutually irreducible decoherence processes regarding different (mutually irreducible) structures of a single closed system [16] is the price that must be paid as long as quantum theory is considered to be universal and complete in a non-interpretational context.…”

Complete Positivity on the Subsystems Level

“…The open quantum systems theory [1,2] is at the core of the modern quantum theory and applications, ranging from the foundational issues [1][2][3][4][5][6][7][8] and quantum optics [1,9] to the cosmological issues [10,11] and the diverse applications, e.g., in quantum technology [12], materials science [13], chemistry and nanotechnology [14][15][16][17] as well as in the nascent field of quantum thermodynamics [18,19].…”