Memory Cost of Quantum Contextuality

Sammanfattning: This is a study taking an information theoretic approach toward quantum contextuality. The approach is that of using the memory complexity of finite-state machines to quantify quantum contextuality. These machines simulate the outcome behaviour of sequential measurements on systems of quantum bits as predicted by quantum mechanics. Of interest is the question of whether or not classical representations by finite-state machines are able to effectively represent the state-independent contextual outcome behaviour. Here we consider spatial efficiency, rather than temporal efficiency as considered by D. Gottesman (1999), for the particular measurement dynamics in systems of quantum bits. Extensions of cases found in the adjacent study of Kleinmann et al. (2010) are established by which upper bounds on memory complexity for particular scenarios are found. Furthermore, an optimal machine structure for simulating any n-partite system of quantum bits is found, by which a lower bound for the memory complexity is found for each n in the natural numbers. Within this finite-state machine approach questions of foundational concerns on quantum mechanics were sought to be addressed. Alas, nothing of novel thought on such concerns is here reported on.