Contextuality and non-locality relations in quantum systems

Official URL: https://risc01.sabanciuniv.edu/record=b2993555_(Table of contents)

Quantum contextuality is the concept that the outcome of a measurement on a system is not always independent of other measurements performed simultaneously on the system. The simplest example where we observe quantum contextuality is the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) measurement scenario which includes a five-measurement state-dependent non-contextuality inequality violated by some qutrit states. We have approached the KCBS inequality from three different perspectives which form the main components of this thesis: (1) We have looked into the symmetries of the KCBS pentagram, i.e., the conservation of quantum contextuality under rotations in the physical space. We work with the quantum systems belonging to the real subgroup of the three-dimensional Hilbert space. We provide the data on Euler rotation angles for maximal quantum contextuality. By using the data, we have found mathematical relations between rotation angles and qutrit states parameterized with spherical coordinates; (2) In the second part of my thesis, we have found the relation between quantum contextuality and concurrence (a measure of entanglement) in the KCBS measurement scenario. We have also found the degree of quantum contextuality for a given concurrence when the KCBS measurements are performed. Using this relation, we have made a comparison between the maximal violations of the classical inequalities (the Bell and KCBS inequalities) for any degree of entanglement. Moreover, we have calculated the degree of violation when maximal entanglement or non-entanglement is observed. We have found a new lower bound for the non-entangled states in the KCBS scenario; (3) After iv discussing the different versions of the quantum delayed-choice experiment, we have introduced a quantum circuit that corresponds to a modified version of the same experiment where one sees that quantum contextuality and entanglement are well correlated with wave and particle properties of a quantum state. This shows that quantum contextuality is in good agreement with the wave-particle duality.