Entanglement and the truncated moment problem

Abstract

We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The algorithm always gives a certificate of entanglement if the state is entangled. If the state is separable, typically a certificate of separability is obtained in a finite number of steps and an explicit decomposition into separable pure states can be extracted.

13 pages

References in corpus (14)

• Entanglement detection
• A complete family of separability criteria
• Taming multiparticle entanglement
• Entanglement and permutational symmetry
• The geometric measure of entanglement for symmetric states
• Detecting multipartite entanglement
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Tensor Representation of Spin States
• Exchange Symmetry and Multipartite Entanglement
• Multiqubit symmetric states with maximally mixed one-qubit reductions
• An improved semidefinite programming hierarchy for testing entanglement
• Multiparticle entanglement as an emergent phenomenon
• Partial transpose criteria for symmetric states
• Quantumness of spin-1 states

Cited by in corpus (14)

• Optimal Entanglement Certification from Moments of the Partial Transpose
• Semidefinite programming relaxations for quantum correlations
• Unveiling quantum entanglement in many-body systems from partial information
• Dimension-free entanglement detection in multipartite Werner states
• Entanglement transitivity problems
• Certifying Quantum Separability with Adaptive Polytopes
• Optimal measurement strategies for fast entanglement detection
• Truncated moment sequences and a solution to the channel separability problem
• Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
• Revealing hidden physical nonclassicality with nonnegative polynomials
• Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• Bound entanglement in symmetric random induced states
• Certifying entanglement dimensionality by $k$-reduction moments
• Quantum Entanglement, Symmetric Nonnegative Quadratic Polynomials and Moment Problems