scholarly journals Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories

PRX Quantum ◽  
2021 ◽  
Vol 2 (1) ◽  
Author(s):  
David Schmid ◽  
John H. Selby ◽  
Elie Wolfe ◽  
Ravi Kunjwal ◽  
Robert W. Spekkens
Keyword(s):  
Generalized Probabilistic Theories ◽  
Probabilistic Theories

Information transfer in generalized probabilistic theories

2015 ◽  
Vol 379 (42) ◽  
pp. 2694-2697 ◽  
Author(s):  
Zhaoqi Wu ◽  
Chuanxi Zhu ◽  
Shunlong Luo ◽  
Jianhui Wang
Keyword(s):  
Information Transfer ◽  
Generalized Probabilistic Theories ◽  
Probabilistic Theories

scholarly journals Generalized Probabilistic Theories in a New Light

2021 ◽  
Author(s):  
Raed Shaiia
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Quantum Mechanical ◽  
Infinite Dimensional ◽  
Classical Systems ◽  
Generalized Probabilistic Theories ◽  
Deterministic Description ◽  
New Formulation ◽  
The Universe ◽  
Probabilistic Theories

Abstract In this paper we will present a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, and give the guidelines to how to extend this work to infinite dimensional Hilbert spaces. Moreover, this new formulation which we will call extended operational-probabilistic theories, applies not only to quantum systems, but also equally well to classical systems, without violating Bell’s theorem, and at the same time solves the measurement problem. This is why we will see that the question of why our universe is quantum mechanical rather than classical is misplaced. The only difference that exists between a classical universe and a quantum mechanical one lies merely in which observables are compatible and which are not. Besides, this extended probability theory which we present in this paper shows that it is non-determinacy, or to be more precise, the non-deterministic description of the universe, that makes the laws of physics the way they are. In addition, this paper shows us that what used to be considered as purely classical systems and to be treated that way are in fact able to be manipulated according to the rules of quantum mechanics –with this new understanding of these rules- and that there is still a possibility that there might be a deterministic level from which our universe emerges, which if understood correctly, may open the door wide to applications in areas such as quantum computing. In addition to all that, this paper shows that without the use of complex vector spaces, we cannot have any kind of continuous evolution of the states of any system.

scholarly journals Probabilistic theories and reconstructions of quantum theory

2021 ◽  
Author(s):  
Markus Müller
Keyword(s):  
Probability Theory ◽  
Quantum Theory ◽  
Three Dimensional ◽  
Complex Numbers ◽  
Classical Probability ◽  
Quantum Bit ◽  
Classical Probability Theory ◽  
Generalized Probabilistic Theories ◽  
Usual Representation ◽  
Probabilistic Theories

These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how physics could be even more general than quantum, I present two conceivable phenomena beyond QT: superstrong nonlocality and higher-order interference. Then I introduce the framework of GPTs, generalizing both quantum and classical probability theory. Finally, I summarize a reconstruction of QT from the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom. In particular, I show why a quantum bit is described by a Bloch ball, why it is three-dimensional, and how one obtains the complex numbers and operators of the usual representation of QT.

scholarly journals Generalized probabilistic theories and conic extensions of polytopes

2014 ◽  
Vol 48 (2) ◽  
pp. 025302 ◽  
Author(s):  
Samuel Fiorini ◽  
Serge Massar ◽  
Manas K Patra ◽  
Hans Raj Tiwary
Keyword(s):  
Generalized Probabilistic Theories ◽  
Probabilistic Theories
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