Operation fidelity explored by numerical range of Kraus operators
arXiv:2212.10139 · doi:10.1103/PhysRevA.108.022409
Abstract
Present-day quantum devices require precise implementation of desired quantum channels. To characterize the quality of implementation one uses the average operation fidelity , defined as the fidelity between an initial pure state and its image with respect to the analyzed operation, averaged over an ensemble of pure states. We analyze statistical properties of the operation fidelity for low-dimensional channels and study its extreme values and probability distribution, both of which can be used for statistical channel discrimination. These results are obtained with help of the joint numerical range of the set of Kraus operators representing a channel. Analytic expressions for the density are derived in some particular cases including unitary and mixed unitary channels as well as quantum maps represented by commuting Kraus operators. Measured distributions of operation fidelity can be used to distinguish between two quantum operations.
arXiv comment14 pages, 5 figures, updated section on probabilistic channel discrimination
References in corpus (31)
- Predicting Many Properties of a Quantum System from Very Few Measurements
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Direct Fidelity Estimation from Few Pauli Measurements
- Practical characterization of quantum devices without tomography
- A Geometric Perspective on Quantum Parameter Estimation
- Fidelity of Single Qubit Maps
- Toolbox for entanglement detection and fidelity estimation
- Average fidelity between random quantum states
- Fundamental limits to quantum channel discrimination
- Variational Quantum Fidelity Estimation
- On the communication complexity of establishing a shared reference frame
- Gate fidelity fluctuations and quantum process invariants
- Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single qubit device
- Optimal estimation of one parameter quantum channels
- Optimal parameter estimation of depolarizing channel
- Direct Fidelity Estimation of Quantum States using Machine Learning
- A Family of Norms With Applications In Quantum Information Theory
- Quantum Algorithm for Fidelity Estimation
- Numerical shadow and geometry of quantum states
- Simple optical measurement of the overlap and fidelity of quantum states: An experiment
- Independent State and Measurement Characterization for Quantum Computers
- Optimal strategies for estimating the average fidelity of quantum gates
- Quantum capacity of bosonic dephasing channel
- On the mixed-unitary rank of quantum channels
- The distribution of quantum fidelities
- Quantum Gate Fidelity in Terms of Choi Matrices
- Discrimination of POVMs with rank-one effects
- Discrimination of dephasing channels
- Regularized maximal fidelity of the generalized Pauli channels
- Regularized maximum pure-state input-output fidelity of a quantum channel
- Real numerical shadow and generalized B-splines