Non-Hermitian extensions of uncertainty relations with generalized metric adjusted skew information

• DOI: 10.1007/s11128-019-2415-2
• Publication Date: 2019-08-21T16:02:41Z
• Authors: Yajing Fan; Huaixin Cao; Wenhua Wang; Huixian Meng; Liang Chen
• Keywords: Operator (biology); Self-adjoint operator

In quantum mechanics, it is well known that the Heisenberg–Schrodinger uncertainty relations hold for two non-commutative observables and density operator. Recently some people start to focus on the uncertainty relations for two non-commutative non-Hermitian operators and density operator. In this paper, we introduce the generalized metric adjusted skew information, generalized metric adjusted correlation measure and the related quantities for non-Hermitian operators. Various properties of them are discussed. Finally, we establish several generalizations of uncertainty relation expressed in terms of the generalized metric adjusted skew information and obtain several results including previous results which can be given as corollaries of our non-Hermitian extensions of Heisenberg-type or Schrodinger-type uncertainty relations.