복잡계의 양자 상관관계

Abstract

The purpose of this thesis is to investigate the quantum correlations in complex systems. The quantum nonlocality and entanglement are the most important features of quantum correlations. We consider the arbitrary number of observers, measurement settings, and high dimensional systems.

We first study the Greenberger-Horne-Zeilinger (GHZ) nonlocality in complex systems and show the conflict between quantum mechanical and local realistic predictions. For the purpose, we employ concurrent observables which are incompatible but still have a common eigenstate. We also suggest the systematic method to construct GHZ nonlocality. Moreover, we propose the generic Bell inequalities in various complex systems. In the study, we show a maximal entangled state exhibits a maximal violation of the Bell inequalities. In continuous variables systems, we show the Bell's theorem for two-mode squeezed state with realizable operations in experiment. For the purpose, we employ the photon presence measurement with the phase shifter, squeezing and displacement operations, and consequently we obtain the larger degree of quantum nonlocality.

The comparison of quantum and classical statistics has provided significant intuitions in understanding quantum mechanics. We suggest an alternative approach to define a commensurate quasiprobability function, by which we can directly compare quantum statistics to the classical. We derive a sufficient condition for the entanglement of two qudits by using the quasiprobability. We also apply it to testing if any given algorithms are classically simulated. We examine well-known quantum algorithms such as Deutsch-Jozsa, Grover and Shor algorithms.