Robertson-Schrodinger-type formulation of Ozawa's noise-disturbance uncertainty principle

Author(s)

Bastos, Catarina ^[1] ; Bernardini, Alex E. ^[2] ; Bertolami, Orfeu ^[3] ; Dias, Nuno Costa ^{[4, 5]} ; Prata, Joao Nuno ^{[4, 5]}

Affiliation

^[1] Inst Super Tecn, Inst Plasmas & Fusao Nucl, P-1049001 Lisbon - Portugal

^[2] Univ Porto, Fac Ciencias, Dept Fis & Astron, P-4169007 Oporto - Portugal

^[3] Univ Porto, Fac Ciencias, Dept Fis & Astron, Ctr Fis Porto, P-4169007 Oporto - Portugal

^[4] Univ Lusofona Humanidades & Tecnol, P-1749024 Lisbon - Portugal

^[5] UL, Grp Fis Matemat, P-1649003 Lisbon - Portugal

• Document type: Journal article
• Source: Physical Review A; v. 89, n. 4 APR 22 2014.
• Web of Science Citations: 17

Abstract

In this work we derive a matrix formulation of a noise-disturbance uncertainty relation, which is akin to the Robertson-Schrodinger uncertainty principle. Our inequality is stronger than Ozawa's uncertainty principle and takes noise-disturbance correlations into account. Moreover, we show that for certain types of measurement interactions it is covariant with respect to linear symplectic transformations of the noise and disturbance operators. Finally, we also study the tightness of our matrix inequality. (AU)

• FAPESP's process: 12/03561-0 - Hamilton (Jacobi) formulation of the dark sector of the universe and contextualized studies on quantum cosmology and non-commutativity
• Grantee: Alex Eduardo de Bernardini
• Support type: Scholarships abroad - Research