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Entanglement-Asymmetry Correspondence for Internal Quantum Reference Frames.

Anne-Catherine de la Hamette1,2, Stefan L Ludescher1,2, Markus P Müller1,2,3

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Internal quantum reference frames are crucial for quantum gravity. Entanglement in these frames directly quantifies system asymmetry, offering insights into imperfect quantum clocks and frames.

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Area of Science:

  • Quantum physics
  • Quantum gravity
  • Gauge theories

Background:

  • Treating reference frames as internal quantum subsystems is vital for quantizing gauge theories and quantum gravity.
  • The Page-Wootters formalism uses a quantum clock to define system evolution via conditioning.

Purpose of the Study:

  • To investigate internal quantum reference frames for arbitrary compact symmetry groups.
  • To establish a quantitative link between entanglement and asymmetry in quantum systems.

Main Methods:

  • Consideration of internal quantum reference frames (R) for quantum systems (S).
  • Analysis of the invariant state on the combined system (RS).
  • Derivation of a quantitative correspondence using conditioning on the reference frame.

Main Results:

  • An exact quantitative duality exists between entanglement in the invariant state of RS and asymmetry in the conditional state of S.
  • This duality holds irrespective of the coherent state system used for conditioning.
  • A representation-theoretic expression is derived for averaging asymmetry.

Conclusions:

  • Entanglement plays a fundamental role in establishing asymmetry within a symmetric quantum world.
  • The derived framework allows unified study of imperfect quantum reference frames, quantum speed limits, and asymmetry typicality.