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The cost of quantum locality.

C A Bédard1

  • 1Università della Svizzera italiana, Via Giuseppe Buffi, 13, 6900 Lugano, Switzerland.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2022
PubMed
Summary

Local descriptions of quantum systems are formally equivalent, but require exponentially increasing degrees of freedom. This study quantifies this cost and investigates supplementary structures to the universal wave function.

Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Foundations of physics

Background:

  • Bell's theorem challenges local descriptions of quantum systems.
  • Previous work by Deutsch and Hayden, and Raymond-Robichaud proposed local quantum system descriptions.
  • The equivalence and cost of these local descriptions remain areas of investigation.

Purpose of the Study:

  • To formally prove the equivalence of different approaches to local quantum system descriptions.
  • To quantify the cost associated with local quantum system descriptions.
  • To investigate structures that may supplement the universal wave function.

Main Methods:

  • Formal proof of equivalence between existing local description methods.
  • Dimensionality analysis to quantify the cost of local descriptions.
Keywords:
localitynon-localityquantum information

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  • Investigation of supplementary structures to the universal wave function.

    • Main Results:

    • All discussed methods for local quantum system description are formally equivalent.
    • The number of degrees of freedom for a local description grows exponentially with system size.
    • The exponential cost is shown to be an expected consequence of local descriptions.

    Conclusions:

    • Local descriptions of quantum systems, while equivalent, incur a significant and expected exponential cost in terms of degrees of freedom.
    • Further investigation into structures supplementing the universal wave function is warranted.