Let A (1),...,A (N) be complex self-adjoint matrices and let rho be a density matrix. The Robertson uncertainty principle [GRAPHICS] 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 <.,.>(rho,) (f) be the associated quantum Fisher information. Based on previous results of several authors, we propose here as a conjecture the inequality [GRAPHICS] whose validity would give a non-trivial bound for any N epsilon N using the commutators i[rho, A(h) ].

Gibilisco, P., Imparato, D., Isola, T. (2008). A volume inequality for quantum Fisher information and the uncertainty principle. JOURNAL OF STATISTICAL PHYSICS, 130(3), 545-559 [10.1007/s10955-007-9454-2].

A volume inequality for quantum Fisher information and the uncertainty principle

GIBILISCO, PAOLO;Isola, T.
2008-01-01

Abstract

Let A (1),...,A (N) be complex self-adjoint matrices and let rho be a density matrix. The Robertson uncertainty principle [GRAPHICS] 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 <.,.>(rho,) (f) be the associated quantum Fisher information. Based on previous results of several authors, we propose here as a conjecture the inequality [GRAPHICS] whose validity would give a non-trivial bound for any N epsilon N using the commutators i[rho, A(h) ].
2008
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Con Impact Factor ISI
generalized variance; uncertainty principle; operator monotone functions; matrix means; quantum Fisher information
Gibilisco, P., Imparato, D., Isola, T. (2008). A volume inequality for quantum Fisher information and the uncertainty principle. JOURNAL OF STATISTICAL PHYSICS, 130(3), 545-559 [10.1007/s10955-007-9454-2].
Gibilisco, P; Imparato, D; Isola, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/41265
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