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

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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.

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Notes

  1. Here we will not discuss the question of the supposed priority of pure states over mixed states: following certain presentations of the theory (e.g., [10]), we will take the generic stance of considering state operators as representing quantum states, and pure states as a particular case.

  2. Wayne Myrvold stressed this point in a comment to our talk at the 14thCongress of Logic, Methodology and Philosophy of Science (Nancy, July 19–26, 2011). We will come back to this point in the next section.

  3. We thank one of the anonymous referees for stressing this point.

  4. The quaternionic formulation of quantum mechanics is a formalism based on quaternion fields instead of complex fields (see [1]).

  5. We are grateful to one of the referees for a comment that suggested this critical remark.

  6. This was the reaction of Rodolfo Gambini when we explained him the basics of modal interpretations. We are grateful to him for the interesting discussion that followed.

  7. We are grateful to one of the referees for giving us the opportunity of emphasizing this point.

  8. Of course, this does not mean that the non-unitary evolution of the open subsystems of a quantum system is due to instability. The analogy emphasized here is based on the fact that both in unstable classical systems and in open quantum systems non-unitarily is obtained as the result of a coarse-graining on a underlying unitary evolution.

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Acknowledgments

This work has been supported by grants of Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET); Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT); and Universidad de Buenos Aires (UBA), Argentina.

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  1. Facultad de Ciencias Exactas y Naturales, CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina

    Sebastian Fortin & Olimpia Lombardi

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  2. Olimpia Lombardi
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Fortin, S., Lombardi, O. Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?. Found Phys 44, 426–446 (2014). https://doi.org/10.1007/s10701-014-9791-3

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