A two-way algorithm for the entanglement problem

Abstract

We propose an algorithm which proves a given bipartite quantum state to be separable in a finite number of steps. Our approach is based on the search for a decomposition via a countable subset of product states, which is dense within all product states. Performing our algorithm simultaneously with the algorithm by Doherty, Parrilo and Spedalieri (which proves a quantum state to be entangled in a finite number of steps) leads to a two-way algorithm that terminates for any input state. Only for a set of arbitrary small measure near the border between separable and entangled states the result is inconclusive.

4 pages, 1 figure

References in corpus (4)

• A complete family of separability criteria
• Distinguishing separable and entangled states
• Largest separable balls around the maximally mixed bipartite quantum state
• Reflections upon separability and distillability

Cited by in corpus (17)

• Quantum entanglement
• Entanglement detection
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Geometrical aspects of entanglement
• The power of symmetric extensions for entanglement detection
• An Introduction to Quantum Entanglement: a Geometric Approach
• A complete criterion for separability detection
• Entanglement and the truncated moment problem
• Minimal tomography with entanglement witnesses
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• An elementary introduction to the geometry of quantum states with pictures
• Many body physics from a quantum information perspective
• Detecting separable states via semidefinite programs
• Constructing all entanglement witnesses from density matrices
• The Essentially Entangled Component of Multipartite Mixed Quantum States, its Properties and an Efficient Algorithm for its Extraction
• Computing finite-dimensional bipartite quantum separability
• Correlation based entanglement criteria for bipartite systems