Relativity of Quantum States and Observables

Abstract

Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.

Current version 3 has an updated bibliography, including a reference to the sequel arXiv:1704.10434

References in corpus (5)

• Reference frames, superselection rules, and quantum information
• Robustness of coherence: An operational and observable measure of quantum coherence
• Robustness of asymmetry and coherence of quantum states
• The WAY theorem and the quantum resource theory of asymmetry
• How to observe a coherent superposition of an atom and a molecule

Cited by in corpus (33)

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• Quantum reference frame transformations as symmetries and the paradox of the third particle
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• A model of quantum spacetime
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• Nonrelativistic spatiotemporal quantum reference frames
• The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• A quantum reference frame size-accuracy trade-off for quantum channels
• Fact-nets: towards a mathematical framework for relational quantum mechanics
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• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks
• Towards a Quantum Erlangen Program
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