Abstract
The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In this work we consider three valued quantum computational logics. More specifically, we will focus on the Hilbert space \(\mathbb C^{3}\), we discuss extensions of several gates to this space and, using the notion of effect probability, we provide a characterization of its states.
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Notes
The extensive definition of a density operator \(\rho \) on \(\mathbb C^3\) is provided in the next section. When a qutrit quantum gate A is applied to a density operator \(\rho \) on \(\mathbb C^3\), the evolution of \( \rho \) is given by: \(A\rho A^{\dagger }\). Since no danger of confusion will be impending, for the sake of notational simplicity, from now on we write \(A(\rho )\).
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Communicated by M.L. Dalla Chiara, R. Giuntini, E. Negri and S. Smets.
The authors acknowledge the support of MIUR within the FIRB project “Structures and Dynamics of Knowledge 24 and Cognition”, Cagliari: F21J12000140001 and of RAS within the project “Modeling the Uncertainty: Quantum Theory and Imaging Processing”.
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Sergioli, G., Ledda, A. A note on many valued quantum computational logics. Soft Comput 21, 1391–1400 (2017). https://doi.org/10.1007/s00500-015-1790-6
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DOI: https://doi.org/10.1007/s00500-015-1790-6