General nonlinear entanglement benchmarks

Entanglement detection plays a central role in quantum information theory. In order to verify entanglement several criteria were developed. By using such criteria one can decide whether a quantum state is entangled or separable. Depending on further specifics of the underlying physical model, some of these criteria might be more suitable (for example in terms of computability and/or experimental effort) than the others. Criteria that are based on entanglement witnesses are mainly used in current experiments. In the proposed project I will investigate the problem of construction of generalized nonlinear entanglement witnesses. The main goal of the project is to develop novel techniques for entanglement verification, techniques which go beyond the traditional ones (e.g. linear entanglement witnesses and their nonlinear extensions) and perform well in situations where only partial information about the physical state can be obtained. In particular, this implies that these new benchmarks can be evaluated without performing state tomography. For this reason, the generalized nonlinear entanglement witnesses will be specifically useful for number of experiments for entanglement detection. Furthermore starting with the bipartite case I will generalize the construction for the multipartite case. In this regard I will particularly concentrate my attention on the detection of genuine multipartite entanglement.

The main focus of this project is to increase the efficiency of the detection of quantum entanglement - one of the most challenging and fascinating properties that can be found in physical states in quantum mechanics. Quantum entanglement is commonly seen from two main perspectives. From the practical perspective the quantum entanglement is an essential resource for many tasks in quantum information science. From a foundational perspective it bears answers to very profound questions about the structure of the quantum physics.The achievements of this project concern both practical and fundamental questions about quantum entanglement. The results about non-linear entanglement witnesses (a method of detecting entangled states), i.e. benchmarks with an increased sensitivity to the entangled states, go in to the first category and are of the practical interest for the current experiments. One of the specific benchmarks developed in this was already successfully applied in two detection experiments. In addition the idea of the general nonlinear entanglement benchmarks leveraged a proposal for the construction of a detector that is capable of entanglement detection in microscopic objects. The results on the structure of multipartite entangled states and the disproval of the Peres conjecture fall into the second category and should be emphasized as well. In the multipartite situation a specific class of states was found that has fundamentally interesting structural properties: the states in this class are composed of states with no entanglement but have to be genuinely multipartite entangled as the whole.Beyond that the results of this project also contribute to entanglement detection in semi-device independent scenario and to optical implementation of quantum communication protocols.