Generalizad probabilistic theories and the foundations of quantum mechanics

FEDERICO HOLIK

Sao Paulo

Workshop; ICTP-SAIFR South American Workshop on the Foundations of Quantum Theory and Cosmology; 2014

Abdus Salam International Centre for Theoretical Physics - South American Institute for Fundamental Research (ICTP-SAIFR)

Generalizad probabilistic theories and the foundations of quantum mechanics Convex operacional models (COMs) [1] were developed in order to represent generalized probabilistic theories. This formalism is general enough as to include classical models and quantum theory as particular cases. It was also used as a tool for comparing quantum mechanics with other possible theories in order to clarify its fundamental aspects. In particular, COMs are widely used for the study of many aspects of quantum information theory and quantum correlations [2]. It is possible to show that many features that were considered as strictly quantum mechanical, were in reality present in other statistical theories [1,2,3,4,5]. In this talk we will discuss the fundamental aspects of the COM approach, its relationships with the quantum logical formalism [6,7], its applications to quantum information theory, and some generalizations [8] of the MaxEnt principle of E. T. Jaynes [9,10,11] which allow for a new systematization of it and reveal important aspects of its geometrical structure. In particular, we will discuss the possibility of developing an axiomatic framework (based on COMs) for the MaxEnt principle, capable of incorporating the action of groups representing physical symmetries. [1] J. Barrett, Information processing in general probabilistic theories, Phys. Rev. A, 75 032304 (2007). [2] S. Popescu, Nonlocality beyond quantum mechanics, Nature Physics, 10, 264?270, (2014). [3] H. Barnum, J. Barrett, M. Leifer and A. Wilce, Cloning and broadcasting in generic probabilistic models, arXiv:quant-ph/061129 (2006). [4] H. Barnum, J. Barrett, M. Leifer and A. Wilce, A general no-cloning theorem, Phys. Rev. Lett., 99 240501 (2007). [5] H. Barnum, J. Barrett, M. Leifer and A. Wilce, Teleportation in general probabilistic theories, Proceedings of Symposia in Applied Mathematics, (2012). [6] F. Holik, C. Massri and A. Plastino, SOP Transactions on Theoretical Physics, Volume 1, Number 2, pp.128-137, (2014). [7] F. Holik, A. Plastino and M. S aenz, Annals Of Physics, Volume 340, Issue 1, 293-310, (2014). [8] F. Holik and A. Plastino, Quantal effects and MaxEnt, J. Math. Phys. 53, 073301 (2012); doi: 10.1063/1.4731769. [9] E. T. Jaynes, Information Theory and Statistical Mechanics, Phys. Rev., 106 (4), 620?630 (1957). [10] E. T. Jaynes, Information Theory and Statistical Mechanics II, Phys. Rev., 108 (2), 171?190 (1957). [11] A. Katz, Principles of Statistical Mechanics: The Information Theory Approach (Freeman, San Francisco, 1967).