Estimation of high-dimensional unitary transformations saturating the Quantum Cramér-Rao bound
arXiv:2310.12699 · doi:10.22331/q-2024-07-10-1405
Abstract
We propose an estimation procedure for -dimensional unitary transformations. For , the unitary transformations close to the identity are estimated saturating the quantum Cramér-Rao bound. For , the estimation of all unitary transformations is also optimal with some prior information. We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography.
Main text: 11 pages, 3 figures. New title, appendix added. Replaced with final version
References in corpus (29)
- Beating the Standard Quantum Limit with Four Entangled Photons
- Quantum Fisher information matrix and multiparameter estimation
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Entanglement-free Heisenberg-limited phase estimation
- Bloch vectors for qudits
- Quantum Enhanced Multiple Phase Estimation
- Compatibility in Multiparameter Quantum Metrology
- State estimation for large ensembles
- Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits
- Entanglement-enhanced measurement of a completely unknown phase
- Unconditional violation of the shot noise limit in photonic quantum metrology
- A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging
- Realization of quantum process tomography in NMR
- Process tomography of ion trap quantum gates
- Multi-parameter estimation beyond Quantum Fisher Information
- Tutorial: Optical quantum metrology
- Quantum process tomography and Linblad estimation of a solid state qubit
- Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation
- Quantum process tomography of unitary and near-unitary maps
- Deterministic realization of collective measurements via photonic quantum walks
- Experimental optical phase measurement approaching the exact Heisenberg limit
- Approaching optimal entangling collective measurements on quantum computing platforms
- Estimation of unitary quantum operations
- Control-enhanced sequential scheme for general quantum parameter estimation at the Heisenberg limit
- Entangling measurements for multiparameter estimation with two qubits
- Efficient computation of the Nagaoka--Hayashi bound for multi-parameter estimation with separable measurements
- Quantum-enhanced tomography of unitary processes
- Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming
- Quantum-Enhanced Sensing from Hyper-Entanglement