Detection of quantum correlations

One of the main foci of modern applied quantum information theory is the production of large-scale quantum entanglement involving many particles, to achieve the next-generation quantum technologies. Although a full-scale quantum computer is still far away in time, in the next few years we can expect to have quantum devices composed of up to a hundred controllable qubits. The primary challenge in moving towards such devices lies in the development of reliable and resource-efficient detection techniques to prove genuine quantum advantage. The main objective of this thesis is to investigate novel methods to detect the presence of quantum correlations in such systems, in particular, quantum entanglement and quantum nonlocality. The first part of this thesis is dedicated to entanglement detection in large-scale quantum systems. Our main goal is to develop a novel probabilistic method in which entanglement is seen as an ability of a quantum system to accomplish certain information-processing tasks. We show that for certain classes of large (e.g. few tens of qubits) quantum states, even a single copy of a quantum state suffices to detect entanglement with a high confidence. Compared to the standard detection methods, this makes our method exceptionally resource-efficient. The developed probabilistic scheme applies to multiple classes of states, vital for quantum computation, such as cluster states or ground states of local Hamiltonians. In the second part of this thesis, we develop a generic framework for translating any entanglement witness into a resource-efficient probabilistic scheme. We show that the confidence level of entanglement detection grows exponentially fast with the number of detection events, which makes this ansatz very efficient and reliable. Furthermore, we present the first experimental performance of our method by verifying the presence of entanglement in a photonic six-qubit cluster state. The third part of this thesis describes the extension of our entanglement verification method to quantum nonlocality. Concrete examples are presented where we convert Bell’s inequalities into the probabilistic procedure and incorporate our method into self-testing schemes. We show that the performance of our method significantly exceeds the ability of the existing methods for detection of quantum nonlocality and self-testing. The last part of this thesis is a study of the weak-convergence properties of random variables generated by quantum measurements. Beginning with a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit distribution of measured relative frequency. We provide the de Finetti-type of representation theorem for all separable states, showing that the measured distribution can be well approximated by a mixture of normal distributions. Additionally, we investigate the convergence rates and show that the relative frequency converges to some constant at the rate of order 1/ √ N for all separable inputs. Finally, we provide an example of a strictly unsharp quantum measurement where we obtain better scaling by using entangled inputs. We find such behaviour of entangled states relevant for quantum information processing.