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1.
Let A
1,…,A
N
be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle
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 〈⋅,⋅〉
ρ,f
be the associated quantum Fisher information. Based on previous results of several authors, we propose here as a conjecture
the inequality
whose validity would give a non-trivial bound for any N∈ℕ using the commutators i[ρ,A
h
]. 相似文献
2.
It is well known that the Cramér–Rao inequality places a lower bound for quantum Fisher information in terms of the variance of any quantum measurement. We establish an upper bound for quantum Fisher information of a parameterized family of density operators in terms of the variance of the generator. These two bounds together yield a generalization of the Heisenberg uncertainty relations from statistical estimation perspective. 相似文献