"** new foundations must give new math**"

from

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**

Firenze

**A basic pair for quantum mechanics**

(joint with **Francesco ValfrÃ©**)

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. ValfrÃ© F., (2007) **Defining a Basic Topology for
Quantum Mechanics** (italian), Laurea Thesis, University of
Padua.