Improved algorithm for quantum separability and entanglement detection

Abstract

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm' for solving the quantum separability problem which follows from the definition of a separable state. By exploiting specific properties of the set of separable states, we introduce a new classical algorithm that solves the problem significantly faster than the `basic algorithm', allowing a feasible separability test where none previously existed e.g. in 3-by-3-dimensional systems. Our algorithm also provides a novel tool in the experimental detection of entanglement.

4 pages, revtex4, no figures

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Cited by in corpus (18)

• Quantum entanglement
• Entanglement detection
• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Geometrical aspects of entanglement
• The power of symmetric extensions for entanglement detection
• Optimal Entanglement Witnesses for Qubits and Qutrits
• An Introduction to Quantum Entanglement: a Geometric Approach
• Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization
• Classification of four-qubit entangled states via Machine Learning
• Cryptography in a Quantum World
• The Quantum Separability Problem for Gaussian States
• Deciding separability with a fixed error
• Characterizing entanglement with geometric entanglement witnesses
• On witnessing arbitrary bipartite entanglement in a measurement device independent way
• Probabilistic state synthesis based on optimal convex approximation
• The Essentially Entangled Component of Multipartite Mixed Quantum States, its Properties and an Efficient Algorithm for its Extraction
• Convex Separation from Optimization via Heuristics
• Decomposition of completely symmetric states states