Analyzing quantum entanglement with the Schmidt decomposition in operator space
arXiv:2304.02447 · doi:10.1103/PhysRevLett.133.040203
Abstract
Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically relies on the observation that quantum states with a high fidelity to some entangled target state are entangled, too. We introduce a general method to construct entanglement witnesses based on the Schmidt decomposition of observables. The method works for two- and, more importantly, many-body systems and is strictly stronger than fidelity-based constructions. The resulting witnesses can also be used to quantify entanglement as well as to characterize the dimensionality of it. Finally, we present experimentally relevant examples, where our approach improves entanglement detection significantly.
arXiv commentS. Denker and C. Zhang contributed equally; 17 pages, one figure
References in corpus (72)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Three qubits can be entangled in two inequivalent ways
- Entanglement of a Pair of Quantum Bits
- Bell nonlocality
- Entanglement detection
- Persistent entanglement in arrays of interacting particles
- Satellite-to-ground quantum key distribution
- On the volume of the set of mixed entangled states
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Quantum state tomography via compressed sensing
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Universal state inversion and concurrence in arbitrary dimensions
- Geometric measure of entanglement and applications to bipartite and multipartite quantum states
- Unextendible Product Bases and Bound Entanglement
- Efficient quantum state tomography
- Optimization of entanglement witnesses
- Quantum Steering
- Classification of mixed three-qubit states
- Experimental ten-photon entanglement
- Witnessing multipartite entanglement
- Direct Fidelity Estimation from Few Pauli Measurements
- Observation of eight-photon entanglement
- A Schmidt number for density matrices
- Entanglement Certification From Theory to Experiment
- Taming multiparticle entanglement
- Entanglement as precondition for secure quantum key distribution
- Further results on the cross norm criterion for separability
- Separability criteria for genuine multiparticle entanglement
- Concurrence of arbitrary dimensional bipartite quantum states
- Experimental device-independent quantum key distribution between distant users
- The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
- Monotones and invariants for multi-particle quantum states
- Schmidt number witnesses and bound entanglement
- Entanglement witnesses: construction, analysis and classification
- The structure of multidimensional entanglement in multipartite systems
- Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
- Four Photon Entanglement from Down Conversion
- Entanglement Witnesses in Spin Models
- Variational Characterisations of Separability and Entanglement of Formation
- Quantum dynamics as a physical resource
- Quantum Overlapping Tomography
- Family of Concurrence Monotones and its Applications
- Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
- Entanglement criteria for Dicke states
- Enhanced entanglement criterion via symmetric informationally complete measurements
- Roofs and Convexity
- Entanglement and nonclassical properties of hypergraph states
- Relaxations of separability in multipartite systems: Semidefinite programs, witnesses and volumes
- Entanglement witness operator for quantum teleportation
- Quantify entanglement by concurrence hierarchy
- Heisenberg-Weyl Observables: Bloch vectors in phase space
- Optimising shadow tomography with generalised measurements
- Class of PPT bound entangled states associated to almost any set of pure entangled states
- Entanglement Detection Beyond Measuring Fidelities
- Concurrence in arbitrary dimensions
- Non-local temporal interferometry for highly resilient free-space quantum communication
- Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs
- Measures of entanglement in multipartite bound entangled states
- Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures
- Geometry of faithful entanglement
- Characterizing entanglement dimensionality from randomized measurements
- Detecting and estimating continuous-variable entanglement by local orthogonal observables
- Probing the geometry of correlation matrices with randomized measurements
- Evaluation of entanglement measures by a single observable
- Separability for mixed states with operator Schmidt rank two
Cited by in corpus (10)
- Semidefinite programming relaxations for quantum correlations
- Enhanced Schmidt number criteria based on correlation trace norms
- Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
- Schmidt number criterion via general symmetric informationally complete measurements
- Multipartite entanglement classes of a multiport beam-splitter
- Measurement-device-independent Schmidt number certification of all entangled states
- Detecting high-dimensional entanglement by randomized product projections
- Formulas for Mutually Orthogonal Quantum States in Two-Qubit Systems: Orthogonal Schmidt Decompositions
- Universal entanglement detection with geometrically optimal witnesses
- On the characterization of partially entanglement breaking and annihilating channels