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Realism defined in EPR paper as “In a complete theory there is an element corresponding to each element of reality.” Bell showed that there is a forbidden triangle (Realism, Quantum Statistics, and Locality), and we are only allowed to pick two out of three. In this thesis, we investigate other inequalities and no-go theorems that we face. We also discuss possible Hidden Variable Models that are tailored to be consistent with Quantum Mechanics and the specific no-go theorems. In the special case of the Leggett Inequality the proposed hidden variable is novel in the sense that the hidden variable is in the measurement device rather than the wave-function.
We study the resources necessary for quantum computation with rebits (qubit states with real amplitudes in the standard basis). We introduce a scheme for universal quantum computation by state injection, and define a Wigner function appropriate for this scheme. We show that the Wigner function obeys a Hudson’s theorem and transforms covariantly under CSS-ness preserving unitary gates; these results allows us to establish that Wigner function negativity is necessary for quantum computation. Furthermore, we establish contextuality as another necessary computational resource. We show that in contrast with the case of qudits [M. Howard et al., Nature 510, 351 (2014)], negativity does not imply contextuality. We discuss state independent contextuality and why it does not arise in our computational scheme.