Workshop on

Quantum Mechanics: Axiomatics of Measurements and connections with Computing and Information Retrieval

Unitary and anti-unitary quantum descriptions of the classical NOT gate

aula 109 - Giovedì 6 Aprile, ore 16.00
  ROBERTO LEPORINI, University of Bergamo

Roberto Leporini is researcher at the University of Bergamo. His research work originates in studies on the theory of conservative computing and quantum gates for finite-valued logics, and presently concerns logics from quantum computation and nanotechnologies.

Roberto Leporini

Two possible quantum descriptions of the classical NOT gate are investigated in the framework of the Hilbert space C2: the unitary and the anti-unitary operator realizations. The two cases are distinguished interpreting the unitary NOT as a quantum realization of the classical gate which on a fixed orthogonal pair of unit vectors, realizing once for all the classical bits 0 and 1, produces the required transformations from 0 to 1 and from 1 to 0 (i.e., logical quantum NOT). The anti-unitary NOT is a quantum realization of a gate which acts as a classical NOT on any pair of mutually orthogonal vectors, each of which is a potential realization of the classical bits (i.e., universal quantum NOT).