2005/10/27 by Masanao Ozawa · 47 citations
Computer Science · Physics and Astronomy · #Entropic uncertainty #Formalism (music) #Noncommutative and Quantum Gravity Theories #Operator (biology) #POVM #Pauli exclusion principle #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum measurement #Relation (database) #SIC-POVM #Uncertainty principle #Weak measurement #quant-ph
paper · pdf · doi:10.1088/1464-4266/7/12/033
published in Journal of Optics B Quantum and Semiclassical Optics 7(12), S672-S681 (IOP Publishing) · 11 pages. Based on the author's invited talk at the 9th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'2005), Besancon, France, May 2-6, 2005
arxiv created 2005/10/27 · openalex publication_date 2005/11/22 · arxiv updated 2010/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise–disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulae for the noise and disturbance of measurements given by measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise–disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals , and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise–disturbance relation.