Partial traces in decoherence and in interpretation: What do reduced states refer to?

Abstract

The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled.

26 pages

References in corpus (13)

• Decoherence, einselection, and the quantum origins of the classical
• Classical Equations for Quantum Systems
• Statistical Mechanics: A Selective Review of Two Central Issues
• Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson
• Toward a Quantum Theory of Observation
• Decoherence, irreversibility and the selection by decoherence of quantum states with definite probabilities
• Galilean and Dynamical Invariance of Entanglement in Particle Scattering
• Tensor Product Structures, Entanglement, and Particle Scattering
• Suppression of decoherence in a generalization of the spin-bath model
• Proper Versus Improper Mixtures: Towards a Quaternionic Quantum Mechanics
• Conditional probabilities and collapse in quantum measurements
• Formal features of a General Theoretical Framework for Decoherence in open and closed systems
• The effect of random coupling coefficients on decoherence

Cited by in corpus (9)

• Measurement, interpretation and information
• Understanding quantum mechanics: a review and synthesis in precise language
• Computing partial traces and reduced density matrices
• Dynamics of algebras in quantum unstable systems
• Quantum decoherence: a logical perspective
• Quantum state reduction of general initial states through spontaneous unitarity violation
• Colored noise driven unitarity violation causing dynamical quantum state reduction
• Perturbative Treatment of Quantum to Classical Transition in Chiral Molecules: Dilute Phase vs. Condensed Phase
• Detection of the genuine non-locality of any three-qubit state