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Environment-Assisted Invariance Does Not Necessitate Born's Rule for Quantum Measurement.

Lotte Mertens1,2, Jasper van Wezel1

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Summary

Environment-assisted invariance (envariance) does not guarantee Born's rule in quantum measurement models. Envariance implies a measurement machine can be constructed for any state to yield Born's rule, resolving paradoxes in linear collapse models.

Keywords:
Born’s ruleenvariancequantum foundations

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Area of Science:

  • Quantum mechanics
  • Foundations of physics
  • Quantum information theory

Background:

  • Environment-assisted invariance (envariance) is a concept used to justify Born's rule in quantum measurement models.
  • Recent findings suggest linear collapse models cannot produce Born's rule, creating a contradiction.

Purpose of the Study:

  • To address the apparent contradiction between envariance and linear collapse models.
  • To clarify the implications of envariance for quantum measurement statistics.

Main Methods:

  • Analysis of assumptions underlying envariance arguments.
  • Development of a model explicitly defining the measurement machine's role.
  • Investigation of the relationship between envariance, measurement machines, and Born's rule.

Main Results:

  • Envariance does not universally imply that all measurements adhere to Born's rule.
  • Envariance implies that for any given quantum state, a specific measurement machine can be constructed to yield Born's rule.
  • This finding aligns with the necessity of nonlinearity in objective collapse models.

Conclusions:

  • The paradox between envariance and linear collapse models is resolved.
  • The role of the measurement apparatus is crucial in understanding the application of envariance.
  • Objective collapse models in quantum mechanics must be nonlinear to be consistent.