Entanglement characterization using quantum designs

Abstract

We present in detail a statistical approach for the reference-frame-independent detection and characterization of multipartite entanglement based on moments of randomly measured correlation functions. We start by discussing how the corresponding moments can be evaluated with designs, linking methods from group and entanglement theory. Then, we illustrate the strengths of the presented framework with a focus on the multipartite scenario. We discuss a condition for characterizing genuine multipartite entanglement for three qubits, and we prove criteria that allow for a discrimination of $W$-type entanglement for an arbitrary number of qubits.

23 pages, 8 figures, Accepted for publication in Quantum

References in corpus (43)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• Entanglement detection
• How to share a quantum secret
• Free-Space distribution of entanglement and single photons over 144 km
• Reference frames, superselection rules, and quantum information
• Photonic quantum information processing: a review
• Probing entanglement entropy via randomized measurements
• Information-theoretic aspects of quantum inseparability of mixed states
• Classification of mixed three-qubit states
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Evenly distributed unitaries: on the structure of unitary designs
• Complete experimental toolbox for alignment-free quantum communication
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Feasibility of satellite quantum key distribution
• Experimental verification of the feasibility of a quantum channel between Space and Earth
• Multipartite generalisation of the Schmidt decomposition
• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
• Cross-Platform Verification of Intermediate Scale Quantum Devices
• Quantum communication without alignment using multiple-qubit single-photon states
• Multipartite entanglement detection from correlation tensors
• Efficient unitary designs with nearly time-independent Hamiltonian dynamics
• Experimentally friendly geometrical criteria for entanglement
• Further results on entanglement detection and quantification from the correlation matrix criterion
• Characterizing multipartite entanglement with moments of random correlations
• Characterizing multipartite entanglement without shared reference frames
• Quantum entanglement from random measurements
• The Clifford group fails gracefully to be a unitary 4-design
• Sinkhorn normal form for unitary matrices
• Efficient Quantum Pseudorandomness
• Multipartite Entanglement Analysis From Random Correlations
• Correlations between outcomes of random measurements
• Transformations of $W$-Type Entangled States
• Correlation tensor criteria for genuine multiqubit entanglement
• Characterizing multipartite entanglement classes via higher-dimensional embeddings
• The maximally entangled set of 4-qubit states
• Noise Thresholds for the [[4, 2, 2]]-concatenated Toric Code
• Random Sampling of Quantum States: A Survey of Methods
• Characterizing quantum states via sector lengths
• Maximum $N$-body correlations do not in general imply genuine multipartite entanglement
• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Reliable experimental quantification of bipartite entanglement without reference frames
• Constraints on correlations in multiqubit systems

Cited by in corpus (26)

• The randomized measurement toolbox
• Symmetry-resolved entanglement detection using partial transpose moments
• Quantum Fisher information from randomized measurements
• Optimal Entanglement Certification from Moments of the Partial Transpose
• Quantum scrambling with classical shadows
• Bound entanglement from randomized measurements
• Machine learning discovery of new phases in programmable quantum simulator snapshots
• Importance sampling of randomized measurements for probing entanglement
• Characterizing entanglement dimensionality from randomized measurements
• Work fluctuations and entanglement in quantum batteries
• Analysing quantum systems with randomised measurements
• Complete characterization of quantum correlations by randomized measurements
• Characterizing correlation within multipartite quantum systems via local randomized measurements
• Statistically significant tests of multiparticle quantum correlations based on randomized measurements
• Collective randomized measurements in quantum information processing
• A Moment for Random Measurements
• Experimental certification of high-dimensional entanglement with randomized measurements
• Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor
• Partial Transpose Moments, Principal Minors and Entanglement Detection
• Quantifying multiparticle entanglement with randomized measurements
• Bipartite quantum state discrimination and decomposable entanglement witness
• Operational detection of entanglement via quantum designs
• Detection of entanglement via moments of positive maps
• Complementarity relations for design-structured POVMs in terms of generalized entropies of order $\alpha \in (0,2)$
• Positive maps from the walled Brauer algebra
• Classification of quantum states of light using random measurements through a multimode fiber