Quantum Reference Frames and the Classification of Rotationally-Invariant Maps
arXiv:0709.0142 · doi:10.1063/1.2884583
Abstract
We give a convenient representation for any map that is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as a resource for performing quantum operations. We introduce the moments of a quantum reference frame, which serve as a complete description of its properties as a frame, and investigate how many times a quantum directional reference frame represented by a spin-j system can be used to perform a certain quantum operation with a given probability of success. We provide a considerable generalization of previous results on the degradation of a reference frame, from which follows a classification of the dynamics of spin-j system under the repeated action of any covariant map with respect to SU(2).
18 pages. Accepted in Journal of Mathematical Physics
References in corpus (13)
- Decoherence Free Subspaces for Quantum Computation
- Reference frames, superselection rules, and quantum information
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Scalable Noise Estimation with Random Unitary Operators
- Programmable quantum gate arrays
- Optimal Cloning of Pure States, Judging Single Clones
- Fidelity of Single Qubit Maps
- Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
- Degradation of a quantum reference frame
- Dynamics of a Quantum Reference Frame
- Optimal measurements for relative quantum information
- Quantum Channels and Representation Theory
- Relative states, quantum axes and quantum references
Cited by in corpus (16)
- Measuring the quality of a quantum reference frame: the relative entropy of frameness
- Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
- Quantum communication using a bounded-size quantum reference frame
- Physics within a quantum reference frame
- A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
- Reexamination of Pure Qubit Work Extraction
- Quantum reference frames and deformed symmetries
- Kinematics and dynamics in noninertial quantum frames of reference
- Quantum theory of polarimetry: From quantum operations to Mueller matrices
- Building all Time Evolutions with Rotationally Invariant Hamiltonians
- Scavenging quantum information: Multiple observations of quantum systems
- Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions
- Universal freezing of asymmetry
- Strong symmetries in collision models and physical dilations of covariant quantum maps
- Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure
- Optimal Quantum Subtracting Machine