The power of symmetric extensions for entanglement detection

Abstract

In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) N -extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.

see Video Abstract at http://www.quantiki.org/video_abstracts/09062731

References in corpus (14)

• Entanglement detection
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• A complete family of separability criteria
• One-and-a-half quantum de Finetti theorems
• Entanglement Theory and the Second Law of Thermodynamics
• Detecting multipartite entanglement
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• Squeezing the limit: Quantum benchmarks for the teleportation and storage of squeezed states
• Quantum Benchmark for Teleportation and Storage of Squeezed States
• Connecting the generalized robustness and the geometric measure of entanglement
• Phase-Covariant Quantum Benchmarks
• Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization
• Optimal probabilistic estimation of quantum states
• Teleportation fidelities of squeezed states from thermodynamical state space measures

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