A Robertson-type Uncertainty Principle and Quantum Fisher Information
| dc.creator | Gibilisco, Paolo | |
| dc.creator | Imparato, Daniele | |
| dc.creator | Isola, Tommaso | |
| dc.date | 2007-07-09 | |
| dc.date.accessioned | 2026-07-07T08:14:38Z | |
| dc.date.available | 2026-07-07T08:14:38Z | |
| dc.description | Let $A_1,...,A_N$ be complex selfadjoint matrices and let $ρ$ be a density matrix. The Robertson uncertainty principle $$ det (Cov_ρ(A_h,A_j)) \geq det (- \frac{i}{2} Tr (ρ[A_h,A_j])) $$ gives a bound for the quantum generalized covariance in terms of the commutators $ [A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $<\cdot, \cdot >_{ρ,f}$ be the associated quantum Fisher information. In this paper we prove the inequality $$ det (Cov_ρ(A_h,A_j)) \geq det (\frac{f(0)}{2} < i[ρ, A_h],i[ρ,A_j] >_{ρ,f}) $$ that gives a non-trivial bound for any $N \in {\mathbb N}$ using the commutators $[ρ,A_h]$. | |
| dc.description | 17 pages (approx.) | |
| dc.identifier | https://arxiv.org/abs/0707.1231 | |
| dc.identifier | http://arxiv.org/abs/0707.1231 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133196 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Statistics Theory | |
| dc.subject | 62B10, 94A17; 46L30, 46L60 | |
| dc.title | A Robertson-type Uncertainty Principle and Quantum Fisher Information | |
| dc.type | text |