Units of rotational information
arXiv:1707.05631 · doi:10.1088/1367-2630/aa94e5
Abstract
Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin.
arXiv comment25 pages + appendix, 7 figures, new results added
References in corpus (45)
- Concentrating Partial Entanglement by Local Operations
- Quantum-enhanced measurements: beating the standard quantum limit
- Reference frames, superselection rules, and quantum information
- Multipartite entanglement and high precision metrology
- Optimal Cloning of Pure States
- Theoretical framework for quantum networks
- Probabilistic cloning and identification of linearly independent quantum states
- Free-space quantum key distribution by rotation-invariant twisted photons
- The resource theory of quantum reference frames: manipulations and monotones
- Programmable quantum gate arrays
- Complete experimental toolbox for alignment-free quantum communication
- Measuring the quality of a quantum reference frame: the relative entropy of frameness
- Optimal Quantum Clocks
- The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
- Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
- Optimal quantum learning of a unitary transformation
- Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
- Efficient use of quantum resources for the transmission of a reference frame
- Bell Measurements and Observables
- Optimal estimation of group transformations using entanglement
- Quantum limits on post-selected, probabilistic quantum metrology
- The WAY theorem and the quantum resource theory of asymmetry
- Optimal estimation of quantum dynamics
- Quantum communication using a bounded-size quantum reference frame
- Optimal cloning of unitary transformations
- Quantum reverse-engineering and reference frame alignment without non-local correlations
- Optimal quantum networks and one-shot entropies
- Fast rate estimation of an unitary operation in SU(d)
- Quantum replication at the Heisenberg limit
- Quantifying the resource of sharing a reference frame
- Optimal design and quantum benchmarks for coherent state amplifiers
- Alignment of reference frames and an operational interpretation for the G-asymmetry
- Optimal quantum operations at zero energy cost
- Cloning the entanglement of a pair of quantum bits
- Quantum learning algorithms for quantum measurements
- Universal super-replication of unitary gates
- Cloning quantum entanglement in arbitrary dimensions
- Deterministic superreplication of one-parameter unitary transformations
- Optimal Probabilistic Simulation of Quantum Channels from the Future to the Past
- Region of fidelities for a 1 -> N universal qubit quantum cloner
- Group representation approach to 1 - N universal quantum cloning machines
- Optimal processing of reversible quantum channels
- Quantum communication, reference frames and gauge theory
- Group theoretic structures in the estimation of an unknown unitary transformation
- Quantum superreplication of states and gates
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- Communication Cost of Quantum Processes
- Quantum-enhanced learning of rotations about an unknown direction
- Breaking global symmetries with locality-preserving operations
- Representation matching for delegated quantum computing
- Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics
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