# An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure

An uncertainty relation in terms of generalized metric adjusted skew information and correlation... The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg’s uncertainty relation and Schrödinger’s uncertainty relation. In this paper, we prove a Schrödinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, \begin{aligned} U_\rho ^{(g,f)}(A)U_\rho ^{(g,f)}(B)\ge \frac{f(0)^2l}{k}\left| \mathrm {Corr}_\rho ^{s(g,f)}(A,B)\right| ^2 \end{aligned} U ρ ( g , f ) ( A ) U ρ ( g , f ) ( B ) ≥ f ( 0 ) 2 l k Corr ρ s ( g , f ) ( A , B ) 2 for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix $$\rho$$ ρ . As applications, we derive some new uncertainty relations for Wigner–Yanase skew information and Wigner–Yanase–Dyson skew information. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure

, Volume 15 (12) – Sep 13, 2016
18 pages

Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1419-4
Publisher site
See Article on Publisher Site

### Abstract

The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg’s uncertainty relation and Schrödinger’s uncertainty relation. In this paper, we prove a Schrödinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, \begin{aligned} U_\rho ^{(g,f)}(A)U_\rho ^{(g,f)}(B)\ge \frac{f(0)^2l}{k}\left| \mathrm {Corr}_\rho ^{s(g,f)}(A,B)\right| ^2 \end{aligned} U ρ ( g , f ) ( A ) U ρ ( g , f ) ( B ) ≥ f ( 0 ) 2 l k Corr ρ s ( g , f ) ( A , B ) 2 for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix $$\rho$$ ρ . As applications, we derive some new uncertainty relations for Wigner–Yanase skew information and Wigner–Yanase–Dyson skew information.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 13, 2016

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