Quantum computational logics are special examples of quantum logic where formulas are supposed to denote pieces of quantum information (qubit-systems or mixtures of qubit-systems), while logical connectives are interpreted as reversible quantum logical gates. Hence, any formula of the quantum computational language represents a synthetic logical description of a quantum circuit. We investigate a many-valued approach to quantum information, where the basic notion of qubit has been replaced by the more general notion of qudit. The qudit-semantics allows us to represent as reversible gates some basic logical operations of Łukasiewicz many-valued logics. In the final part of the article we discuss some problems that concern possible implementations of gates by means of optical devices

A many-valued approach to quantum computational logics

GIUNTINI, ROBERTO;SERGIOLI, GIUSEPPE;
2018-01-01

Abstract

Quantum computational logics are special examples of quantum logic where formulas are supposed to denote pieces of quantum information (qubit-systems or mixtures of qubit-systems), while logical connectives are interpreted as reversible quantum logical gates. Hence, any formula of the quantum computational language represents a synthetic logical description of a quantum circuit. We investigate a many-valued approach to quantum information, where the basic notion of qubit has been replaced by the more general notion of qudit. The qudit-semantics allows us to represent as reversible gates some basic logical operations of Łukasiewicz many-valued logics. In the final part of the article we discuss some problems that concern possible implementations of gates by means of optical devices
2018
Quantum logics; Quantum tomography; logical gates
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/213909
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