Detecting entanglement of unknown quantum states with random measurements

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.

Detecting entanglement of unknown continuous variable states with random measurements

“…Without adding any information about the states, we still found a reduction in the number of measurements needed to certify the presence of entanglement. The phenomenology of entanglement detection in random CV states is very similar to the case of decomposable witnesses for discrete systems [16]. Hence, a higher entanglement is easier to detect, but in our case this improvement is not as significant as in the discrete case.…”

“…Therefore, the best strategy in this case would be to perform random measurements, serving as building blocks for the construction of an entanglement witness by means of a semidefinite optimization algorithm. This idea is inspired by an analogous method for the discrete-variable case, which was developed in [16].…”

Entanglement detection on an NMR quantum-information processor using random local measurements

“…al. [31] to construct a class of decomposable entanglement witness operators for an unknown state using random local measurements. In this protocol, once we fix the set of measurements, the witness is optimized to increase the possibility of detecting entanglement.…”

“…(2) as described in [31]. However, in our case we will first choose the measurements that we want to experimentally perform and then optimize the witness operator in such a way that we maximize the chances of detecting entanglement.…”

“…The method assumes some prior knowledge of the density matrix and is able to unequivocally detect entanglement by performing only a few local measurements [28][29][30]. These entanglement detection schemes have been recently extended to the case of completely unknown states with no prior information [31]. This scheme uses a set of random local measurements and optimizes over the space of possible entanglement witnesses that can be constructed thereof.…”