Abstract
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.
Highlights
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
We focus on finite sets of measurements on quantum states, 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
Summary
Violate a given EW inequality does not exclude the existence of a different violated inequality involving the same data, yet to be discovered This may erroneously suggest that entanglement witnessing is limited by creativity and physical insight and that the entanglement witnessing problem (“is a quantum dataset compatible with a separable state?”) [5,6,7] is generically undecidable. The parameters K 1⁄4 fKagRa1⁄41—the coupling constants of the classical field theory—are Lagrange multipliers whose optimization allows one to build the separable state ρp whose expectation values fhAaiρpg best approximate the quantum data fhAaiρg.
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