David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Guillaume Adenier (ed.) (2007). Quantum Theory, Reconsideration of Foundations 4: Växjö (Sweden), 11-16 June, 2007. American Institute of Physics.
Frederick M. Kronz (1990). Hidden Locality, Conspiracy and Superluminal Signals. Philosophy of Science 57 (3):420-444.
Itamar Pitowsky (2003). Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability. Studies in History and Philosophy of Science Part B 34 (3):395-414.
Rob Clifton & Damian Pope, On the Nonlocality of the Quantum Channel in the Standard Teleportation Protocol.
Larry S. Temkin (1986). Inequality. Philosophy and Public Affairs 15 (2):99-121.
Fred Kronz, Range of Violations of Bell’s Inequality by Entangled Photon Pairs Entangled Photon Pairs.
Jeffrey Bub & Vandana Shiva (1978). Non-Local Hidden Variable Theories and Bell's Inequality. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:45 - 53.
Added to index2009-01-28
Total downloads28 ( #74,164 of 1,692,491 )
Recent downloads (6 months)2 ( #111,548 of 1,692,491 )
How can I increase my downloads?