"new foundations must give new math"

from "The Basic Picture. Structures for constructive topology"

by Giovanni Sambin, Oxford University Press, forthcoming


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Under the patronage of

Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Italy

University of Padova, Italy

AILA (Italian Association of Logic and Applications), whose first president was Giovanni Sambin (from 1987 to 1994).

Abstracts » Battilotti

Giulia Battilotti

A basic pair for quantum mechanics
(joint with Francesco Valfré)

We define a basic pair in Hilbert spaces, illustrating a fundamental relation between states and observables in quantum mechanics.

We briefly discuss it, with particular attention to the holistic treatment of information, due to entangled states, that can be focused thanks to the duality of basic pairs.

This finds a correspondence with a solution found in sequent calculi for quantum computation.

Hopefully, it will help in finding a positive and contructive characterization of entangled states, fundamental for the quantum computational speed up, rather than the negative definition proposed in Hilbert spaces.

Battilotti G., (2008) Interpreting quantum superposition by sequents, to be submitted to Proc. IQSA08.

Dalla Chiara M.L., Giuntini R., Leporini R., (2006) Compositional and Holistic Quantum Computational Semantics, Natural Computing.

Sambin G., (2008) The Basic Picture. Structures for constructive topology, Oxford University Press.

In press. Valfré F., (2007) Defining a Basic Topology for Quantum Mechanics (italian), Laurea Thesis, University of Padua.