Optimal entanglement witnesses: a scalable data-driven approach
- URL: http://arxiv.org/abs/2101.02038v3
- Date: Tue, 20 Jul 2021 17:40:14 GMT
- Title: Optimal entanglement witnesses: a scalable data-driven approach
- Authors: Ir\'en\'ee Fr\'erot and Tommaso Roscilde
- Abstract summary: We focus on finite sets of measurements on quantum states (hereafter called quantum data)
We propose an approach which, given a particular spatial partitioning of the system of interest, can effectively ascertain whether or not the data set is compatible with a separable state.
When compatibility is disproved, the approach produces optimal entanglement witness for the quantum data at hand.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Multipartite entanglement is the 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 data set is compatible with a separable state.
When compatibility is disproved, 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.
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