Constructing monotones for quantum phase references in totally dephasing channels

Understand

Restrictions on quantum operations give rise to resource theories.

• Total lack of a shared reference frame for transformations associated with a group G between two parties is equivalent to having, in effect, an invariant channel between the parties and a corresponding superselection rule.
• The resource associated with the absence of the reference frame is known as "frameness" or "asymmetry." We show that any entanglement monotone for pure bipartite states can be adapted as a pure-state frameness monotone for phase-invariant channels [equivalently U(1) superselection rules] and extended to the case of mixed states via the convex-roof extension.
• As an application, we construct a family of concurrence monotones for U(1) frameness for general finite-dimensional Hilbert spaces.