Constructing monotones for quantum phase references in totally dephasing channels

Abstract

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.

10 pages

References in corpus (6)

• Reference frames, superselection rules, and quantum information
• The resource theory of quantum reference frames: manipulations and monotones
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Classical and quantum communication without a shared reference frame
• Quantum communication using a bounded-size quantum reference frame
• Entanglement of Collaboration

Cited by in corpus (20)

• Observable measure of quantum coherence in finite dimensional systems
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Quantum speed limits, coherence and asymmetry
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Alternative framework for quantifying coherence
• Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
• Measure-Independent Freezing of Quantum Coherence
• A general framework for quantum macroscopicity in terms of coherence
• Quantum secure direct communication with private dense coding using general preshared quantum state
• The asymmetry properties of pure quantum states
• Ordering states with coherence measures
• The Wigner-Yanase information can increase under phase sensitive incoherent operations
• Symmetrizing Cost of Quantum States
• Simulating Symmetric Time Evolution With Local Operations
• Universal freezing of asymmetry
• Superdense Coding in Resource Theory of Asymmetry
• Quantifying Algebraic Asymmetry of Hamiltonian Systems
• Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics
• Asymmetry and dynamical criticality