91 research outputs found
Additive monotones for resource theories of parallel-combinable processes with discarding
A partitioned process theory, as defined by Coecke, Fritz, and Spekkens, is a
symmetric monoidal category together with an all-object-including symmetric
monoidal subcategory. We think of the morphisms of this category as processes,
and the morphisms of the subcategory as those processes that are freely
executable. Via a construction we refer to as parallel-combinable processes
with discarding, we obtain from this data a partially ordered monoid on the set
of processes, with f > g if one can use the free processes to construct g from
f. The structure of this partial order can then be probed using additive
monotones: order-preserving monoid homomorphisms with values in the real
numbers under addition. We first characterise these additive monotones in terms
of the corresponding partitioned process theory.
Given enough monotones, we might hope to be able to reconstruct the order on
the monoid. If so, we say that we have a complete family of monotones. In
general, however, when we require our monotones to be additive monotones, such
families do not exist or are hard to compute. We show the existence of complete
families of additive monotones for various partitioned process theories based
on the category of finite sets, in order to shed light on the way such families
can be constructed.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Noncontextual wirings
Contextuality is a fundamental feature of quantum theory and is necessary for
quantum computation and communication. Serious steps have therefore been taken
towards a formal framework for contextuality as an operational resource.
However, the most important component for a resource theory - a concrete,
explicit form for the free operations of contextuality - was still missing.
Here we provide such a component by introducing noncontextual wirings: a
physically-motivated class of contextuality-free operations with a friendly
parametrization. We characterize them completely for the general case of
black-box measurement devices with arbitrarily many inputs and outputs. As
applications, we show that the relative entropy of contextuality is a
contextuality monotone and that maximally contextual boxes that serve as
contextuality bits exist for a broad class of scenarios. Our results complete a
unified resource-theoretic framework for contextuality and Bell nonlocality
- …