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Quantum computational logics provide a fertile common ground for a uniied treatment of vagueness and uncertainty. In this paper we describe an approach to the logic of quantum computation that has been recently taken up and developed by the present authors. Special attention will be devoted to a generalisation of Chang's MV algebras (called quasi-MV… (More)

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational… (More)

Quantum computation and quantum computational logics are intrinsically connected with some puzzling epistemic problems. In the framework of a quantum computational approach to epistemic logic we investigate the following question: is it possible to interpret the basic epis-temic operations (having information, knowing) as special kinds of Hilbert-space… (More)

Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like " Alice knows that Bob does not understand that π is irrational " as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic… (More)

Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic… (More)

- MARIA LUISA DALLA, GIUSEPPE SERGIOLI, Anatolij Dvurečenskij
- 2014

Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, qureg-isters or mixtures of quregisters), while logical connectives correspond to (quantum logical) gates that transform quantum information in a reversible way.… (More)

- Iuris Antiqui, Marco Giunti, Giuseppe Sergioli, Giuliano Vivanet
- 2013

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In this paper we discuss an approach to quantum computation where the basic information units (qubits and quregisters) are replaced by density operators and the restriction to unitary operators as logical gates is lifted through the introduction of the more general concept of quantum operation ([17], [1]). This perspective is especially suited to provide a… (More)