Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?

Foundations of Physics 44 (4):426-446 (2014)

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
Keywords Quantum state  Reduced state  Partial trace  Decoherence   No-collapse interpretations
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DOI 10.1007/s10701-014-9791-3
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References found in this work BETA

How the Laws of Physics Lie.Nancy Cartwright - 1983 - Oxford University Press.
How the Laws of Physics Lie.Nancy Cartwright - 1985 - Philosophy of Science 52 (3):478-480.
Interpreting the Quantum World.Jeffrey Bub - 1998 - British Journal for the Philosophy of Science 49 (4):637-641.
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Citations of this work BETA

A New Application of the Modal-Hamiltonian Interpretation of Quantum Mechanics: The Problem of Optical Isomerism.Sebastian Fortin, Olimpia Lombardi & Juan Camilo Martínez González - 2018 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 62:123-135.
Quantum Decoherence: A Logical Perspective.Sebastian Fortin & Leonardo Vanni - 2014 - Foundations of Physics 44 (12):1258-1268.

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