Optimal Entanglement Witnesses: A Scalable Data-Driven Approach

Multipartite entanglement is a key resource allowing quantum devices to outperform their classical counterparts, and entanglement certification is fundamental to assess any quantum advantage. The only scalable certification scheme relies on entanglement witnessing, typically effective only for speci...

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Bibliographic Details
Published in:Physical review letters 2021-07, Vol.127 (4), p.1-040401, Article 040401
Main Authors: Frérot, Irénée, Roscilde, Tommaso
Format: Article
Language:English
Subjects:
Certification
Compatibility
Entangled states
Field theory
Mapping
Physics
Polynomials
Quantum entanglement
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Summary:Multipartite entanglement is a key resource allowing quantum devices to outperform their classical counterparts, and entanglement certification is fundamental to assess any quantum advantage. The only scalable certification scheme relies on entanglement witnessing, typically effective only for special entangled states. Here, we focus on finite sets of measurements on quantum states (hereafter called quantum data), and we propose an approach which, given a particular spatial partitioning of the system of interest, can effectively ascertain whether or not the dataset is compatible with a separable state. When compatibility is disproven, the approach produces the optimal entanglement witness for the quantum data at hand. Our approach is based on mapping separable states onto equilibrium classical field theories on a lattice and on mapping the compatibility problem onto an inverse statistical problem, whose solution is reached in polynomial time whenever the classical field theory does not describe a glassy system. Our results pave the way for systematic entanglement certification in quantum devices, optimized with respect to the accessible observables.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.127.040401