2001/06/24 by Gordon N. Fleming, Fleming, Gordon N. · 1 citation
Chemistry · Computer Science · Physics and Astronomy · #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #General Physics (physics.gen-ph) #History and advancements in chemistry #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #physics.atom-ph #physics.gen-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.physics/0106077
21 pages
openalex publication_date 2001/06/24 · arxiv created 2001/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It generalizes the rule of the orthogonality of eigenvectors for distinct eigenvalues and is shown to imply all the Robertson generalized uncertainty relations. It severely constrains the difference between probabilities obtained from 'close' quantum states and the different responses they can have to unitary transformations. Thus, it is dubbed a master inequality. With appropriate definitions the inequality also holds throughout general probability theory and appears not to be well known there either. That classical inequality is obtained here in an appendix. The quantum inequality can be obtained from the classical version but a more direct quantum approach is employed here. A similar but weaker classical inequality has been reported by Uffink and van Lith.