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 epistemic operations (having information, knowing) as special kinds of Hilbert-space operations? We show that non-trivial knowledge operations cannot be represented by unitary operators. We introduce the notions of strong epistemic quantum computational structure and of epistemic quantum computational structure, where knowledge operations are identified with special examples of quantum operations. This represents the basic tool for developing an epistemic quantum computational semantics, where epistemic sentences (like “Alice knows that the spin-value in the x-direction is up”) are interpreted as quantum pieces of information that may be stored by quantum objects.
Titolo: | Epistemic quantum computational structures in a Hilbert-space environment |
Tutti gli autori: | Beltrametti, Enrico; Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto; Sergioli, Giuseppe |
Data di pubblicazione: | 2012 |
Abstract (eng): | 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 epistemic operations (having information, knowing) as special kinds of Hilbert-space operations? We show that non-trivial knowledge operations cannot be represented by unitary operators. We introduce the notions of strong epistemic quantum computational structure and of epistemic quantum computational structure, where knowledge operations are identified with special examples of quantum operations. This represents the basic tool for developing an epistemic quantum computational semantics, where epistemic sentences (like “Alice knows that the spin-value in the x-direction is up”) are interpreted as quantum pieces of information that may be stored by quantum objects. |
Rivista: | |
Nelle collezioni: | 1.1.01 Articoli/Saggi in rivista - Journal Articles/Essays |
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Epistemic.pdf | publisher's version - versione editoriale | Licenza default Aisberg | Testo non consultabile |