Optimal estimation of quantum dynamics

Abstract

We construct the optimal strategy for the estimation of an unknown unitary transformation $U\in SU(d)$. This includes, in addition to a convenient measurement on a probe system, finding which is the best initial state on which $U$ is to act. When $U\in SU(2)$, such an optimal strategy can be applied to estimate simultaneously both the direction and the strength of a magnetic field, and shows how to use a spin 1/2 particle to transmit information about a whole coordinate system instead of only a direction in space.

4 pages, REVTEX

Cited by in corpus (64)

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• Efficient use of quantum resources for the transmission of a reference frame
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• Quantum entanglement from random measurements
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• Ultimate limits for multiple quantum channel discrimination
• Entanglement is not very useful for estimating multiple phases
• Fast rate estimation of an unitary operation in SU(d)
• Entanglement-enhanced testing of multiple quantum hypotheses
• Estimation of pure qubit states with collective and individual measurements
• Quantum-enhanced tomography of unitary processes
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• Experimental quantum reading with photon counting
• Entanglement assisted alignment of reference frames using a dense covariant coding
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Extremal covariant POVM's
• Remote Implementation of Quantum Operations
• Optimal Universal Quantum Error Correction via Bounded Reference Frames
• Improved discrimination of unitaries by entangled probes
• Query-optimal estimation of unitary channels in diamond distance
• Optimal joint estimation of multiple Rabi frequencies
• Discrete outcome quantum sensor networks
• Enhancing sensitivity in quantum metrology by Hamiltonian extensions
• Multiparameter estimation via an ensemble of spinor atoms
• Comparison of unitary transforms
• Units of rotational information
• Quantum advantage of time-reversed ancilla-based metrology of absorption parameters
• Secure alignment of coordinate systems by using quantum correlation
• Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation
• Optimal environment localization
• Optimal quantum discrimination of single-qubit unitary gates between two candidates
• No-iteration of unknown quantum gates
• Entanglement-assisted communication in the absence of shared reference frame
• Attainability of the Holevo-Cramér-Rao bound for two-qubit 3D magnetometry
• Estimation of two-qubit interactions through channels with environment assistance
• Ultimate limits of approximate unambiguous discrimination
• Mutually Unbiased Unitary Bases of Operators on $d$-dimensional Hilbert Space
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• Limitation of maximally entangled probes for single-shot distinguishability of unitaries
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• Agnostic Process Tomography
• Constructions of mutually unbiased entangled bases
• Quantum Advantage in Storage and Retrieval of Isometry Channels
• On the query complexity of unitary channel certification
• Bounding the benefit of adaptivity in quantum metrology using the relative fidelity
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