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A Dynamic-Logical Perspective on Quantum Behavior

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Abstract

In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various forms of classical information flow: the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system.

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References

  1. Abramsky, S., and B. Coecke, ‘A Categorical Semantics of Quantum Protocols’, in the proceedings of the 19th IEEE conference on Logic in Computer Science (LiCS’04). Available at arXiv:quant-ph/0402130.

  2. Aerts, D., ‘Description of compound physical systems and logical interaction of physical systems’, in E.G. Beltrametti, and B. C. van Fraassen (eds.), Current Issues on Quantum Logic, Ettore Majorana, International Science Series, Physical Sciences, vol. 8. Dordrecht: Kluwer Academic, 1981, pp. 381–405

  3. Amira H., Coecke B. and Stubbe I. (1998). ‘How Quantales Emerge by Introducing Induction within the Operational Approach’. Helvetica Physica Acta 71: 554–572

    Google Scholar 

  4. Baltag A. and Moss L. (2004). ‘Logics for Epistemic Programs’. Synthese 139: 165–224

    Article  Google Scholar 

  5. Baltag, A., L. Moss, and H. van Ditmarsch, ‘Epistemic Logic and Information Update’, Handbook on the Philosophy of Information, in press.

  6. Baltag, A., and S. Smets, ‘Complete Axiomatizations of Quantum Actions’, International Journal of Theoretical Physics 44(12):2267–2282, 2005. Available at (http://www.vub.ac.be/CLWF/SS/IQSA.pdf)

  7. Baltag, A., and S. Smets, ‘The Logic of Quantum Programs’, in P. Selinger (ed.), Proceedings of the 2nd International Workshop on Quantum Programming Languages (QPL2004), TUCS General Publication 33:39–56 Turku Center for Computer Science, 2004. PHILSCI00001799

  8. Baltag, A., and S. Smets, ‘LQP: The Dynamic Logic of Quantum Information’, in Mathematical Structures in Computer Science, Special Issue on Quantum Programming Languages 16(3):491–525, 2006.

  9. Baltag, A., and S. Smets, ‘What can Logic Fearn from Quantum Mechanics?’, paper presented at ECAP2005, available at (http://www.vub.ac.be/CLWF/SS/ECAP.pdf)

  10. Baltag, A., and S. Smets, ‘Conditional Doxastic Models: A Qualitative Approach to Dynamic Belief Revision’, in G. Mints and R. de Queiroz (eds.), Electronic Notes in Theoretical Computer Science 165:5–21, 2006.

  11. Baltag, A., and S. Smets, ‘The Logic of Conditional Doxastic Actions: A Theory of Dynamic Multi-Agent Belief Revision’, in S. Artemov and R. Parikh (eds.), Proceedings of the Workshop on Rationality and Knowledge, ESSLLI 2006.

  12. Baltag, A., and S. Smets, ‘Dynamic Belief Revision over Multi-Agent Plausibility Models’, in G. Bonanno, W. van de Hoek, and M. Woolridge (eds.), 7th Conference on Logic and the Foundations of Game and Decision, Liverpool, 2006.

  13. Baltag, A., and S. Smets, ‘A Qualitative Theory of Dynamic Interactive Belief Revision’, Submitted for publication to G. Bonanno, W. van der Hoek, and M.Wooldridge (eds.), Texts in Logic and Games, Amsterdam University Press.

  14. Baltag, A., and S. Smets, ‘Probabilistic Dynamic Belief Revision’, to appear in J. van Benthem, S. Ju, and F. Veltman (eds.), College Publications, London 2007.

  15. Bell J.S. (1964). ‘On the Einstein Podolsky Rosen Paradox’. Physics 1: 195–200

    Google Scholar 

  16. van Benthem, J., ‘Dynamic Logic for Belief Revision’, ILLC Tech Report. DARE electronic archive, University of Amsterdam, 2006. To appear in Journal of Applied Non-Classical Logics.

  17. van Benthem J. (1996). Exploring Logical Dynamics, Studies in Logic, Language and Information. CSLI Publications, Stanford

    Google Scholar 

  18. Birkhoff G. and von Neumann J. (1936). ‘The Logic of Quantum Mechanics’. Annals of Mathematics 37: 823–843

    Article  Google Scholar 

  19. Coecke, B., ‘The Logic of Entanglement’, Research Report, March 2004, arXiv:quant-ph/0402014.

  20. Coecke, B., D.J. Moore, and S. Smets, ‘Logic of Dynamics & Dynamics of Logic; Some Paradigm Examples’, in S. Rahman, J. Symons, D.M. Gabbay, and J.P. Van Bendegem (eds.), Logic, Epistemology and the Unity of Science 527–556, 2004.

  21. Coecke B., Moore D.J. and Stubbe I. (2001). ‘Quantaloids Describing Causation and Propagation for Physical Properties’. Foundations of Physics Letters 14: 357–367. arXiv:quant-ph/0009100

    Article  Google Scholar 

  22. Coecke B. and Smets S. (2004). ‘The Sasaki Hook is not a [Static] Implicative Connective but Induces a Backward [in Time] Dynamic One that Assigns Causes’. International Journal of Theoretical Physics 43: 1705–1736. (arXiv: quant-ph/0111076)

    Article  Google Scholar 

  23. Coecke B. and Stubbe I. (1999). ‘On a Duality of Quantales Emerging from an Operational Resolution’. International Journal of Theoretical Physics 38: 3269–3281

    Article  Google Scholar 

  24. Daniel W. (1982). ‘On the Non-Unitary Evolution of Quantum Systems’. Helvetica Physica Acta 55: 330–338

    Google Scholar 

  25. Daniel W. (1989). ‘Axiomatic Description of Irreversible and Reversible Evolution of a Physical System’. Helvetica Physica Acta 62: 941–968

    Google Scholar 

  26. Einstein A., Podolsky B. and Rosen N. (1935). ‘Can Quantum Mechanical Description of Reality Be Considered Complete?’. Physical Review 47: 777–80

    Article  Google Scholar 

  27. Fagin, R., J. Halpern, Y. Moses, and M. Vardi, Reasoning about Knowldege, MIT Press, 1995.

  28. Faure CL.-A., Moore D.J. and Piron C. (1995). ‘Deterministic Evolutions and Schrodinger Flows’. Helvetica Physica Acta 68: 150–157

    Google Scholar 

  29. Gärdenfors P. (1988). Knowledge in Flux. MIT Press, Cambridge MA

    Google Scholar 

  30. Harel, D., D. Kozen, and J. Tiuryn, Dynamic Logic, MIT Press, 2000.

  31. Hughes R.I.G. (1989). The Structure and Interpretation of Quantum Mechanics. Harvard University Press, Massachusetts

    Google Scholar 

  32. Maudlin, T., Quantum Non-Locality and Relativity, Blackwell Oxford, 1994.

  33. Pauli, W., Handbuch der Physik, Vol.5, Part 1: Prinzipien der Quantentheorie 1, 1958; English translation by P. Achuthan and K. Venkatsesan, General Principles of Quantum Mechanics, Springer Verlag, Berlin, 1980.

  34. Piron C. (1976). Foundations of Quantum Physics. W.A. Benjamin Inc., Massachusetts

    Google Scholar 

  35. Smets, S., ‘From Intuitionistic Logic to Dynamic Operational Quantum Logic’, Poznan Studies in Philosophy and the Humanities, vol. 91, 2006.

  36. Spekkens, R.W., ‘In defense of the epistemic view of quantum states: a toy theory’, arXiv:quant-ph/0401052v2 ,2005.

  37. Valckenborgh, F., ‘Compound Systems in Quantum Axiomatics’, Doctoral Thesis, Vrije Universiteit Brussel, 2001.

  38. von Neumann, J., Grundlagen der Quantenmechanik, Springer Verlag, Berlin, 1932. (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, New Jersey, 1996)

  39. Zeilinger A. (1999) ‘A Foundational Principle for Quantum Mechanics’. Foundations of Physics 29(4):631-643

    Article  Google Scholar 

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Authors and Affiliations

  1. Computing Laboratory, Oxford University, Oxford, UK

    A. Baltag

  2. Center for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussel, Belgium

    S. Smets

  3. IEG, Research Group on the Philosophy of Information, Oxford University, Oxford, UK

    S. Smets

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  1. A. Baltag
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  2. S. Smets
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Correspondence to S. Smets.

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Baltag, A., Smets, S. A Dynamic-Logical Perspective on Quantum Behavior. Stud Logica 89, 187–211 (2008). https://doi.org/10.1007/s11225-008-9126-5

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