Networks of quantum reference frames and the nature of conserved quantities

Abstract

We show that networks of quantum frames of reference, in which one frame may be used to produce multiple other frames that in their turn prepare systems which may interact with one another, have counterintuitive properties that make following the exchange of conserved quantities very subtle, and raise questions about the very nature of conserved quantities. In addition, we present an alternative approach to analysing quantum reference frames that we believe will be useful in discussions related to quantum frames of reference.

Figures (3)

• Figure 1: Chains of system preparations. (a) A grand-frame $G$ prepares a frame $F$, which then prepares a system $S$. (b) A grand-frame $G$ prepares two frames, $F$ and $F'$, which in turn prepare systems $S$ and $S'$, respectively.
• Figure 2: Simple networks of quantum frames of reference. (a) Two frames prepare each a system, which are individually measured. (b) Similar, except from the fact that the two systems interact before their measurement.
• Figure 3: Conservation laws in networks of quantum frames of references. Note that the proofs in the text consider only a single $F$ and a single $F'$, but they apply in full generality. (a) In a simple chain, the conservation law for individual outcomes is local between the measured system and its frame of reference. (b) In a network, so long as there is no interaction between different branches, the conservation law for individual outcomes remains localised. (c) However, if systems in distinct branches interact before their measurement, the conservation law for individual outcomes requires the inclusion of every frame up to and including their first common grand-frame in the network.