In the qubit semantics the meaning of any sentence α is represented by a quregister: a unit vector of the n–fold tensor product ⊗n ℂ^2, where n depends on the number of occurrences of atomic sentences in α (see Cattaneo et al.). The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence α gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of α can be regarded as a quantum circuit that transforms the quregister associated to the occurrences of atomic subformulas of α into the quregister associated to α.
Dalla Chiara, M., Giuntini, R., Leporati, A., Leporini, R. (2005). Qubit Semantics and Quantum Trees. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 44(7), 971-983 [10.1007/s10773-005-7074-7].
Qubit Semantics and Quantum Trees
LEPORATI, ALBERTO OTTAVIO;
2005
Abstract
In the qubit semantics the meaning of any sentence α is represented by a quregister: a unit vector of the n–fold tensor product ⊗n ℂ^2, where n depends on the number of occurrences of atomic sentences in α (see Cattaneo et al.). The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence α gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of α can be regarded as a quantum circuit that transforms the quregister associated to the occurrences of atomic subformulas of α into the quregister associated to α.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.