Statistical Methods for Quantum State Verification and Fidelity Estimation
arXiv:2109.10805 · doi:10.1002/qute.202100126
Abstract
The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource-efficient manner. In this article we present a review of the recent progress in this field. We first explain how the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing. Then, we explain in detail various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication. Finally, we discuss several extensions of the problem, such as the certification of quantum channels and the verification of entanglement.
23 pages, 10 figures, close to the published version
References in corpus (27)
- Entanglement detection
- Scalable multi-particle entanglement of trapped ions
- Multi-party entanglement in graph states
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Direct Fidelity Estimation from Few Pauli Measurements
- Detecting Genuine Multipartite Entanglement with Two Local Measurements
- Entanglement Certification From Theory to Experiment
- Quantum state discrimination and its applications
- Entanglement purification and quantum error correction
- Entanglement Detection in the Stabilizer Formalism
- Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
- Permutationally invariant quantum tomography
- Bell Inequalities for Graph States
- Toolbox for entanglement detection and fidelity estimation
- Graphs, Quadratic Forms, and Quantum Codes
- Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
- Entanglement and nonclassical properties of hypergraph states
- Encoding Hypergraphs into Quantum States
- Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
- Sample-efficient device-independent quantum state verification and certification
- Precision-Guaranteed Quantum Metrology
- Efficient verification of entangled continuous-variable quantum states with local measurements
- Versatile fidelity estimation with confidence
- Efficient Experimental Verification of Quantum Gates with Local Operations
- Proof-of-principle experimental demonstration of quantum gate verification
- Toward Instance-Optimal State Certification With Incoherent Measurements
- Optimal Verification of the Bell State and Greenberger-Horne-Zeilinger States in Untrusted Quantum Networks
Cited by in corpus (27)
- Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
- Analysing quantum systems with randomised measurements
- Robust and efficient verification of graph states in blind measurement-based quantum computation
- Certifying the Topology of Quantum Networks: Theory and Experiment
- Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
- Efficient Verification of Ground States of Frustration-Free Hamiltonians
- Collective Operations Can Exponentially Enhance Quantum State Verification
- Quantum reservoir computing for photonic entanglement witnessing
- Cross-Platform Verification in Quantum Networks
- A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method
- Experimental optimal verification of three-dimensional entanglement on a silicon chip
- Efficient verification of arbitrary entangled states with homogeneous local measurements
- Cross-Platform Comparison of Arbitrary Quantum Processes
- Nondestructive Verification of Entangled States via Fidelity Witnessing
- Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation
- Q-fid: Quantum Circuit Fidelity Improvement with LSTM Networks
- Experimental Verification of Entangled States in the Adversarial Scenario
- Error estimation of different schemes to measure spin-squeezing inequalities
- Towards Quantum Universal Hypothesis Testing
- Scalable Experimental Bounds for Entangled Quantum State Fidelities
- Protecting entanglement witnesses with randomized measurements
- Why cut-and-choose quantum state verification cannot be both efficient and secure
- Ability of entanglement and purity to help to detect systematic experimental errors
- Beating the Optimal Verification of Entangled States via Collective Strategies
- Structure of quantum measurements implementable with one round of classical communication
- Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases
- Prescriptive preparation and verification of nonstabilizer states