Objectivity In Different Quantum Reference Frames

Quantum Darwinism and its frameworks describe objectivity of quantum systems via their information in the environment. However, the observation of these environments must be done with respect to a frame of reference. Given so, is objectivity consistent across different reference frames? Here, we take the quantum reference frame structure of [1] and consider the scenario where system and environment are static particles distributed across space. In this prescription, entanglement and coherence are interchangeable frame-dependent properties, and statistical mixedness and classical correlations are equivalently interchangeable. We find that the consistency of objectivity depends on the distinguishability of states in all relevant quantum reference frames, which in turn depends on non-degenerate relative separations, sharp localisation, and sufficiently large macro-fractions.

[1] F. Giacomini, E. Castro-Ruiz, and C. Brukner, “Quantum mechanics and the covariance of physical laws in quantum reference frames”, Nat. Commun. 10, 494 (2019)