Uncertainty Principle and Quantum Fisher Information - II

Uncertainty Principle and Quantum Fisher Information - II
Paolo Gibilisco∗, Daniele Imparato† and Tommaso Isola‡
April 20, 2007
Abstract
Heisenberg and Schrödinger uncertainty principles give lower bounds for the product of variances
Varρ (A) · Varρ (B) if the observables A, B are not compatible, namely if the commutator [A, B] is
not zero.
In this paper we prove an uncertainty principle in Schrödinger form where the bound for the
product of variances Varρ (A) · Varρ (B) depends on the area spanned by the commutators i[ρ, A] and
i[ρ, B] with respect to an arbitrary quantum version of the Fisher information.
∗ Dipartimento SEFEMEQ, Facoltà di Economia, Università di Roma “Tor Vergata”, Via Columbia 2, 00133 Rome,
Italy. Email: [email protected] – URL: http://www.economia.uniroma2.it/sefemeq/professori/gibilisco
† Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy.
Email:
[email protected]
‡ Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Rome, Italy.
Email: [email protected] URL: http://www.mat.uniroma2.it/∼isola
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