3 research outputs found
Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
Superselection rules (SSRs) limit the mechanical and quantum processing
resources represented by quantum states. However SSRs can be violated using
reference systems to break the underlying symmetry. We show that there is a
duality between the ability of a system to do mechanical work and to act as a
reference system. Further, for a bipartite system in a globally symmetric pure
state, we find a triality between the system's ability to do local mechanical
work, its ability to do ``logical work'' due to its accessible entanglement,
and its ability to act as a shared reference system.Comment: 5 pages, no figures. Extended resubmitted version. Slightly modified
title. Transferred to PR
The resource theory of quantum reference frames: manipulations and monotones
Every restriction on quantum operations defines a resource theory,
determining how quantum states that cannot be prepared under the restriction
may be manipulated and used to circumvent the restriction. A superselection
rule is a restriction that arises through the lack of a classical reference
frame and the states that circumvent it (the resource) are quantum reference
frames. We consider the resource theories that arise from three types of
superselection rule, associated respectively with lacking: (i) a phase
reference, (ii) a frame for chirality, and (iii) a frame for spatial
orientation. Focussing on pure unipartite quantum states (and in some cases
restricting our attention even further to subsets of these), we explore
single-copy and asymptotic manipulations. In particular, we identify the
necessary and sufficient conditions for a deterministic transformation between
two resource states to be possible and, when these conditions are not met, the
maximum probability with which the transformation can be achieved. We also
determine when a particular transformation can be achieved reversibly in the
limit of arbitrarily many copies and find the maximum rate of conversion. A
comparison of the three resource theories demonstrates that the extent to which
resources can be interconverted decreases as the strength of the restriction
increases. Along the way, we introduce several measures of frameness and prove
that these are monotonically nonincreasing under various classes of operations
that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio