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Sum of Entanglement and Subsystem Coherence Is Invariant under Quantum Reference Frame Transformations.

Carlo Cepollaro1,2, Ali Akil3, Paweł Cieśliński4

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This summary is machine-generated.

Quantum reference frames (QRFs) reveal that entanglement and subsystem coherence trade-off, forming a QRF invariant. This invariant clarifies how quantum resources, like entanglement, are responsible for Bell

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Area of Science:

  • Quantum Information Theory
  • Quantum Foundations
  • Quantum Gravity

Background:

  • Quantum reference frames (QRFs) transform superposition and entanglement.
  • Understanding resource changes under QRF transformations is crucial for quantum information processing.

Purpose of the Study:

  • To prove the existence of a QRF invariant capturing the trade-off between entanglement and subsystem coherence.
  • To analyze the implications of this interplay for Bell's inequality violations.

Main Methods:

  • Demonstration of the invariance of the sum of entanglement and subsystem coherence for specific resource quantifiers.
  • Identification of a weaker trade-off applicable to any pair of measures.

Main Results:

  • A QRF invariant is proven, quantifying the trade-off between entanglement and subsystem coherence.
  • A general, weaker trade-off relation is established for any chosen measures.
  • The quantum resource responsible for Bell's inequality violations is identified for any QRF.

Conclusions:

  • The study establishes a fundamental interplay between entanglement and subsystem coherence within QRFs.
  • Findings enhance the understanding of quantum information-theoretic aspects of QRFs.
  • Provides a foundation for future research in quantum theory and quantum gravity.