Approximating relational observables by absolute quantities: A quantum accuracy-size trade-off

TL;DR

This paper explores how large quantum reference systems can approximate relative observables with absolute quantities, highlighting a trade-off between quantum accuracy and system size.

Contribution

It introduces conditions under which absolute quantities can effectively approximate relational observables in quantum systems, emphasizing the importance of reference system size.

Findings

Large reference systems enable good approximation of relational observables

Quantum accuracy improves with increasing reference system size

Trade-off exists between system size and measurement precision

Abstract

The notion that any physical quantity is defined and measured relative to a reference frame is traditionally not explicitly reflected in the theoretical description of physical experiments where, instead, the relevant observables are typically represented as "absolute" quantities. However, the emergence of the resource theory of quantum reference frames as a new branch of quantum information science in recent years has highlighted the need to identify the physical conditions under which a quantum system can serve as a good reference. Here we investigate the conditions under which, in quantum theory, an account in terms of absolute quantities can provide a good approximation of relative quantities. We find that this requires the reference system to be large in a suitable sense.