Abstract
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the use of random local measurements, from which entanglement witnesses are then constructed via semidefinite programming methods. We propose a scheme of successively increasing the number of measurements until the presence of entanglement can be unambiguously concluded, and investigate its performance in various examples.
Highlights
Entanglement is a valuable resource for accomplishing quantum information tasks with a performance exceeding what can be optimally achieved classically
We have proposed a new method to detect the entanglement of quantum states, about which nothing is known except the dimension, using random local measurements
A witness operator is constructed by means of a semidefinite optimization procedure, minimizing the expectation value in a way that ensures that the operator is a valid witness at all times
Summary
Entanglement is a valuable resource for accomplishing quantum information tasks with a performance exceeding what can be optimally achieved classically. A method to characterize entanglement in such a case is given by quantum tomography [7], i.e., reconstructing the full density matrix from a pre-chosen set of measurements. If one is merely interested in the question of whether a given state is entangled, full tomography yields an excess of information; it may be feasible to extract the required knowledge using fewer measurements. An approach in this direction was proposed in Ref.
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