Observer-Dependent Entropy and Diagonal R\'enyi Invariants in Quantum Reference Frames

TL;DR

This paper introduces a family of observer-independent diagonal R'enyi entropies in quantum reference frames, revealing fundamental limits on how different quantum observers can assign entropy to the same system.

Contribution

It identifies frame-independent entropies and provides a quantitative framework for understanding observer-dependent entropy in quantum systems.

Findings

Frame-independent diagonal R'enyi entropies exist for arbitrary subsystems.

Observer-dependence of entropy decomposes into coherence and inter-frame correlations for ideal frames.

Bounds on entropy disagreement depend on the effective relational Hilbert space dimension.

Abstract

Quantum reference frames provide a relational description of multipartite quantum systems in which physical states and observables are defined relative to quantum observers. Yet different observers can assign different entropies to the same system, raising the question of how such observer-dependence is constrained. We identify a family of frame-independent diagonal R\'enyi entropies for arbitrary subsystems, yielding a generalized multipartite coherence-entanglement tradeoff. For ideal frames, the observer-dependence of subsystem entropy admits an exact decomposition into a sum of single-frame coherences and inter-frame correlations; for non-ideal frames, it is instead bounded by the dimension of an effective relational Hilbert space determined by the representation structure of the frames. Our results place quantitative limits on how much quantum observers can disagree about subsystem entropy, with potential implications for observer-dependent entropy assignments in gravitational settings.