How to observe duality in entanglement of two distinguishable particles?

TL;DR

This paper explores how duality in entanglement can be observed in distinguishable particles using reference frames, challenging superselection rule limitations and with implications for quantum resource theories.

Contribution

It demonstrates conditions under which duality in entanglement of distinguishable particles can be observed via reference frames, bypassing superselection rules.

Findings

Duality in entanglement can be observed in distinguishable particles with appropriate reference frames.

Superselection rules can be bypassed using special auxiliary states.

Implications for resource theories of quantum entanglement.

Abstract

The entanglement between two bosons or fermions can be accessed if there exists an auxiliary degree of freedom which can be used to label and effectively distinguish the two particles. For some types of entanglement between two indistinguishable particles one can observe duality, i.e., if the entanglement is present in the Hilbert space H and an auxiliary Hilbert space H' is used to label the particles, then if we used H as a label the entanglement would be present in H'. For distinguishable particles this effect does not occur because of superselection rules which prevent superpositions of different types of particles. However, it is known that superselection rules can be bypassed if one uses special auxiliary states that are known as reference frames. Here we study properties of reference frames which allow for an observation of a duality in entanglement between two distinguishable particles. Finally, we discuss the consequences of this result from the resource-theoretic point of view.