Analysing quantum systems with randomised measurements
arXiv:2307.01251 · doi:10.1016/j.physrep.2024.09.009
Abstract
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum computing when dealing with noisy environments, and allow the estimation of properties of complex quantum systems in an easy and efficient manner. In this review, we present the advancements made in utilising randomised measurements in various scenarios of quantum information science. We describe how to detect and characterise different forms of entanglement, including genuine multipartite entanglement and bound entanglement. Bell inequalities are discussed to be typically violated even with randomised measurements, especially for a growing number of particles and settings. Furthermore, we also present an overview on the estimation of non-linear functions of quantum states and shadow tomography from randomised measurements. Throughout the review, we complement the description of theoretical ideas by explaining key experiments.
review paper, 56 pages, 9 figures, P. Cieśliński and S. Imai contributed equally as co-first authors
References in corpus (204)
- Quantum entanglement
- A computable measure of entanglement
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Bell nonlocality
- Many body localization and thermalization in quantum statistical mechanics
- Entanglement detection
- On the Measurement of Qubits
- Device-independent security of quantum cryptography against collective attacks
- Quantum metrology with nonclassical states of atomic ensembles
- Significant-loophole-free test of Bell's theorem with entangled photons
- The logarithmic negativity: A full entanglement monotone that is not convex
- A strong loophole-free test of local realism
- Quantum Resource Theories
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Quantum state tomography via compressed sensing
- Symmetric Informationally Complete Quantum Measurements
- Multi-party entanglement in graph states
- Bell inequalities for arbitrarily high dimensional systems
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Quantum spin squeezing
- Quantum metrology from a quantum information science perspective
- Unknown Quantum States and Operations, a Bayesian View
- General Monogamy Inequality for Bipartite Qubit Entanglement
- Quantum Fisher information matrix and multiparameter estimation
- On mutually unbiased bases
- From Bell's Theorem to Secure Quantum Key Distribution
- Efficient quantum state tomography
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Four qubits can be entangled in nine different ways
- Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
- Non-locality and Communication Complexity
- Probing entanglement entropy via randomized measurements
- Fisher information and multiparticle entanglement
- Classification of mixed three-qubit states
- Quantum information can be negative
- All multipartite Bell correlation inequalities for two dichotomic observables per site
- Direct Fidelity Estimation from Few Pauli Measurements
- Chaos and complexity by design
- The Bloch Vector for N-Level Systems
- Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
- Universal Quantum Estimator
- Direct estimations of linear and non-linear functionals of a quantum state
- Bell's theorem for general N-qubit states
- Bloch vectors for qudits
- Evenly distributed unitaries: on the structure of unitary designs
- The randomized measurement toolbox
- Entanglement Certification From Theory to Experiment
- Detection of Symmetry Protected Topological Phases in 1D
- Entanglement as precondition for secure quantum key distribution
- Random Quantum Circuits are Approximate 2-designs
- Further results on the cross norm criterion for separability
- Mixed-state entanglement from local randomized measurements
- Local random quantum circuits are approximate polynomial-designs
- Certified randomness in quantum physics
- Quantum state merging and negative information
- Device-independent witnesses of genuine multipartite entanglement
- Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
- Direct detection of quantum entanglement
- Multipartite entanglement in spin chains
- Absolute Maximal Entanglement and Quantum Secret Sharing
- Permutationally invariant quantum tomography
- Reference frame independent quantum key distribution
- Optimal spin squeezing inequalities detect bound entanglement in spin models
- Spin squeezing and pairwise entanglement for symmetric multiqubit states
- The definition of multipartite nonlocality
- Symmetries of the Bell correlation inequalities
- Quantifying entanglement resources
- The structure of multidimensional entanglement in multipartite systems
- Entropic uncertainty relations and entanglement
- Entangled three-qubit states without concurrence and three-tangle
- Magnetic Susceptibility as a Macrosopic Entaglement Witness
- How to generate random matrices from the classical compact groups
- Reflections upon separability and distillability
- Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions
- Four Photon Entanglement from Down Conversion
- Quantum fidelity measures for mixed states
- An observable entanglement measure for unknown mixed quantum states
- Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
- Cross-Platform Verification of Intermediate Scale Quantum Devices
- Absolutely maximally entangled states of seven qubits do not exist
- The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
- Detection of multipartite entanglement in the vicinity of symmetric Dicke states
- Machine Learning Assisted Many-Body Entanglement Measurement
- The Two Bell's Theorems of John Bell
- Optimal verification of entangled states with local measurements
- Permutationally invariant state reconstruction
- Lifting Bell inequalities
- Optimizing quantum process tomography with unitary 2-designs
- Models of quantum complexity growth
- Generalized Euler Angle Paramterization for SU(N)
- Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
- Do all pure entangled states violate Bell's inequalities for correlation functions?
- Unitary designs and codes
- Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
- Genuine Network Multipartite Entanglement
- Single-copies estimation of entanglement negativity
- Quantum Correlation Without Classical Correlations
- Entanglement in mutually unbiased bases
- Symmetry-resolved dynamical purification in synthetic quantum matter
- Experimental Estimation of Quantum State Properties from Classical Shadows
- Many-body topological invariants from randomized measurements
- All entangled pure states violate a single Bell's inequality
- Universal observable detecting all two-qubit entanglement and determinant based separability tests
- Experimental single-setting quantum state tomography
- Metrological Detection of Multipartite Entanglement from Young Diagrams
- Efficient and feasible state tomography of quantum many-body systems
- Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices
- Majorization criterion for distillability of a bipartite quantum state
- Optimal Entanglement Certification from Moments of the Partial Transpose
- Looking for symmetric Bell inequalities
- Nonclassical correlations from randomly chosen local measurements
- Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
- Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
- Further results on entanglement detection and quantification from the correlation matrix criterion
- Entanglement barrier and its symmetry resolution: theory and experiment
- Characterizing multipartite entanglement with moments of random correlations
- Conditional entropies and their relation to entanglement criteria
- Correlation complementarity yields Bell monogamy relations
- Experimental quantum state measurement with classical shadows
- Quantum key distribution based on private states: unconditional security over untrusted channels with zero quantum capacity
- Device-independent tomography of multipartite quantum states
- The Church of the Symmetric Subspace
- Heat Capacity as A Witness of Entanglement
- Characterizing multipartite entanglement without shared reference frames
- Statistical Methods for Quantum State Verification and Fidelity Estimation
- Single-copy entanglement detection
- Heisenberg-Weyl Observables: Bloch vectors in phase space
- Characterizing Genuine Multilevel Entanglement
- Quantum entanglement from random measurements
- The Clifford group fails gracefully to be a unitary 4-design
- Optimising shadow tomography with generalised measurements
- Energy and multipartite entanglement in multidimensional and frustrated spin models
- Quantifying Bell non-locality with the trace distance
- Quantum scrambling with classical shadows
- Shadow process tomography of quantum channels
- Two-photon speckle as a probe of multi-dimensional entanglement
- There is no anomaly in the nonlocality of two entangled qutrits
- Bound entanglement from randomized measurements
- Multipartite Entanglement Analysis From Random Correlations
- Correlations between outcomes of random measurements
- Experimental few-copy multi-particle entanglement detection
- Experimental bilocality violation without shared reference frames
- Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
- Detecting entanglement in quantum many-body systems via permutation moments
- Multipartite fully-nonlocal quantum states
- Geometry of faithful entanglement
- Generating nonclassical correlations without fully aligning measurements
- Characterizing entanglement dimensionality from randomized measurements
- Composite parameterization and Haar measure for all unitary and special unitary groups
- Work fluctuations and entanglement in quantum batteries
- An Experimentally accessible geometric measure for entanglement in -qubit pure states
- Non-classicality thresholds for multiqubit states - numerical analysis
- Multipartite entanglement detection with minimal effort
- Efficient algorithm for multi-qudit twirling for ensemble quantum computation
- All CHSH polytopes
- Genuine Multipartite Entanglement without Multipartite Correlations
- Observers can always generate nonlocal correlations without aligning measurements by covering all their bases
- Multipartite nonlocality and random measurements
- k-stretchability of entanglement, and the duality of k-separability and k-producibility
- Entanglement characterization using quantum designs
- Detecting genuine multipartite entanglement of pure states with bipartite correlations
- Entropic uncertainty relations from quantum designs
- Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits
- Experimentally Violating Bell Inequalities Without Complete Reference Frames
- Towards an equivalence between maximal entanglement and maximal quantum nonlocality
- Experimental Schmidt Decomposition and Entanglement Detection
- Complete characterization of quantum correlations by randomized measurements
- Chaos and random matrices in supersymmetric SYK
- Characterizing quantum states via sector lengths
- Matrix integrals over unitary groups: An application of Schur-Weyl duality
- Survey on the Bell nonlocality of a pair of entangled qudits
- Statistically significant tests of multiparticle quantum correlations based on randomized measurements
- Maximum -body correlations do not in general imply genuine multipartite entanglement
- Probing the geometry of correlation matrices with randomized measurements
- Enhanced estimation of quantum properties with common randomized measurements
- Construction of mutually unbiased bases with cyclic symmetry for qubit systems
- Entanglement detection with trace polynomials
- Positive maps and trace polynomials from the symmetric group
- Collective randomized measurements in quantum information processing
- Examining the dimensionality of genuine multipartite entanglement
- -uniform mixed states
- Incompatible local hidden-variable models of quantum correlations
- Genuine -partite entanglement without -partite correlation functions
- Optimal tests of genuine multipartite nonlocality
- Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames
- The Mathematics of Entanglement
- Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios
- Higher dimensional entanglement without correlations
- Entanglement phase diagrams from partial transpose moments
- Reliable experimental quantification of bipartite entanglement without reference frames
- A Moment for Random Measurements
- Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads
- Optimized state independent entanglement detection based on geometrical threshold criterion
- Some Ulam's reconstruction problems for quantum states
- Correlation constraints and the Bloch geometry of two qubits
- Experimentally friendly approach towards nonlocal correlations in multisetting N -partite Bell scenarios
- Bell inequality violations with random mutually unbiased bases
- Quantifying multiparticle entanglement with randomized measurements
- Valid and efficient entanglement verification with finite copies of a quantum state
- Stretching the limits of multiparticle entanglement
- McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions
- Experimental verification of bound and multiparticle entanglement with the randomized measurement toolbox
- Refuting spectral compatibility of quantum marginals
Cited by in corpus (23)
- Krylov shadow tomography: Efficient estimation of quantum Fisher information
- Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
- Experimental certification of high-dimensional entanglement with randomized measurements
- Metrological usefulness of entanglement and nonlinear Hamiltonians
- Approximate inverse measurement channel for shallow shadows
- Real randomized measurements for analyzing properties of quantum states
- Detecting genuine multipartite entanglement using moments of positive maps
- Entanglement dynamics and Page curves in random permutation circuits
- Geometry of two-body correlations in three-qubit states
- Protecting entanglement witnesses with randomized measurements
- Detecting high-dimensional entanglement by randomized product projections
- Variational-toolbox-based separability detection of multiqubit states
- Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
- How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?
- Absolutely maximally entangled pure states of multipartite quantum systems
- Learning mixed quantum states in large-scale experiments
- Inter-qubit correlation dynamics driven by mutual interactions
- Multiqubit monogamy relations beyond shadow inequalities
- Optimal randomized measurements for a family of non-linear quantum properties
- Scalable protocol to coherence estimation from scarce data: Theory and experiment
- Certifying entanglement dimensionality by -reduction moments
- Reference-frame-independent quantum metrology
- Classification of quantum states of light using random measurements through a multimode fiber