Quantum resource covariance

TL;DR

This paper develops a theoretical framework demonstrating that quantum resources can be considered invariant under certain transformations, challenging the notion of absolute physical reality in quantum mechanics.

Contribution

It introduces a relational symmetry principle and quantum reference frames to establish quantum resource covariance, expanding understanding of quantum invariants.

Findings

Quantum resources can be made Galilean invariant.

More than coherence and correlations are needed for resource covariance.

Quantum reality is not absolute, but frame-dependent.

Abstract

The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval -- whose value all inertial observers agree upon. This reveals, so to speak, a genuine "fact" of the universe, a relativistic invariant. On the other hand, since the dawn of quantum mechanics, there is no consensus on what the theory is all about. The situation is admittedly subtler: quantum theory is grounded on a complex vector space and the very notions of observer and reference frame are controversial. Here we construct a theoretical framework within which a given combination of quantum resources is shown to be a Galilean invariant. To this end, we postulate a principle of relational symmetry between "the observer" and "the observed" and employ the notion of quantum reference frame. Unitary transformations then follow that allow us to perceive the physical resources seen from the viewpoint of any quantum system. Interestingly, we find that one needs more than quantum coherence and quantum correlations to prove quantum resources covariance. Finally, we show that the notion of physical reality implied by quantum mechanics is not absolute.