The resource theory of quantum reference frames: manipulations and monotones

Abstract

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.

37 pages, 4 figures, Published Version

References in corpus (8)

• Reference frames, superselection rules, and quantum information
• Entanglement constrained by superselection rules
• Degradation of a quantum reference frame
• Fundamentals of universality in one-way quantum computation
• Relativistically invariant quantum information
• How to observe a coherent superposition of an atom and a molecule
• Entanglement under restricted operations: Analogy to mixed-state entanglement
• Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond

Cited by in corpus (21)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Entanglement Theory and the Second Law of Thermodynamics
• Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
• Geometric lower bound for a quantum coherence measure
• The WAY theorem and the quantum resource theory of asymmetry
• Quantum communication using a bounded-size quantum reference frame
• Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
• The Wigner-Yanase information can increase under phase sensitive incoherent operations
• Kinematics and dynamics in noninertial quantum frames of reference
• Distinguishability measures between ensembles of quantum states
• Building all Time Evolutions with Rotationally Invariant Hamiltonians
• Quantum parameter estimation with imperfect reference frames
• Non-thermal quantum channels as a thermodynamical resource
• Quantifying Spatial Correlations of General Quantum Dynamics
• Simulating Symmetric Time Evolution With Local Operations
• Optimal asymptotic cloning machines
• Quantum Resource Theory for Charge-Parity-Time Inversion
• Time-reversal frameness and superselection