The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations

Abstract

Recent work on quantum reference frames (QRFs) has demonstrated that superposition and entanglement are properties that change under QRF transformations. Given their utility in quantum information processing, it is important to understand how a mere change of perspective can produce or reduce these resources. Here we find a trade-off between entanglement and subsystem coherence under a QRF transformation, in the form of a conservation theorem for their sum, for two pairs of measures. Moreover, we find a weaker trade-off for any possible pair of measures. Finally, we discuss the implications of this interplay for violations of Bell's inequalities, clarifying that for any choice of QRF, there is a quantum resource responsible for the violation. These findings contribute to a better understanding of the quantum information theoretic aspects of QRFs, offering a foundation for future exploration in both quantum theory and quantum gravity.

5 pages, 1 figure, 8 pages of Supplementary Material

References in corpus (15)

• Entanglement detection
• Device-independent security of quantum cryptography against collective attacks
• Measuring Quantum Coherence with Entanglement
• Reference frames, superselection rules, and quantum information
• Device-independent quantum key distribution secure against collective attacks
• The resource theory of quantum reference frames: manipulations and monotones
• Private Randomness Expansion With Untrusted Devices
• Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
• Detecting and estimating coherence based on coherence witnesses
• Quantum Reference Frames at the Boundary of Spacetime
• Quantum reference frames for an indefinite metric
• Operational Quantum Reference Frame Transformations
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Quantum Reference Frames for Lorentz Symmetry
• Quantum conformal symmetries for spacetimes in superposition

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