Constructing monotones for quantum phase references in totally dephasing channels

Journal Article · Mon Aug 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.84.022322· OSTI ID:22068515

Toloui, Borzu; Sanders, Barry C ^[1]; Gour, Gilad ^[1]

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1. Institute for Quantum Information Science, University of Calgary, Alberta T2N 1N4 (Canada)

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. Furthermore, we study ''frameness of formation'' for mixed states analogous to entanglement of formation. In the case of a qubit, we show that it can be expressed as an analytical function of the concurrence analogously to the Wootters formula for entanglement of formation. Our results highlight deep links between entanglement and frameness resource theories.

• OSTI ID: 22068515
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 84; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HILBERT SPACE
MIXED STATES
PURE STATES
QUANTUM ENTANGLEMENT
SUPERSELECTION RULES