Trace inequalities on a generalized Wigner–Yanase skew information

Abstract

Keywords:Trace inequality Wigner-Yanase skew information Wigner-Yanase-Dyson skew information and uncertainty relation We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S. Luo for the quantum uncertainty quantity excluding the classical mixture. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued.

Comments on conjectures of trace inequalities on a generalized Wigner–Yanase skew information

“…To describe one parameter extended versions for the inequality (2.1), we introduce some definitions [1,4,7].…”

“…In [1], the authors obtained the uncertainty relation for a generalized Wigner-Yanase skew information:…”

“…Furuichi, Yanagi and Kuriyama gave the following conjectures of trace inequalities on the Wigner-Yanase-Dyson skew information and a generalized Wigner-Yanase skew information in [1]. …”

“…The relation between these quantities and the uncertainty relation was studied in [4,7]. In [1,7], Furuichi et al introduced a new generalized Wigner-Yanase skew information…”

“…(a) (See Conjecture 2.3 of [1].) For α ∈ [0, 1], ρ ∈ D 1 n and A, B ∈ M n,sa , does the inequality (b) (See Conjecture 2.10 of[1].) For α ∈ [0, 1], ρ ∈ D 1 n and A, B ∈ M n,sa , does the inequality…”