By Giulio Chiribella, Robert W. Spekkens
This publication offers the 1st unified evaluate of the burgeoning learn sector on the interface among Quantum Foundations and Quantum details. themes comprise: operational choices to quantum idea, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent beneficial properties of the set of quantum correlations.
Powered via the injection of unpolluted principles from the sphere of Quantum info and Computation, the rules of Quantum Mechanics are in the course of a renaissance. The final 20 years have obvious an explosion of latest effects and learn instructions, attracting huge curiosity within the clinical neighborhood. the range and variety of assorted methods, in spite of the fact that, makes it difficult for a newcomer to acquire a huge photo of the sector and of its high-level pursuits. the following, fourteen unique contributions from best specialists within the box hide probably the most promising learn instructions that experience emerged within the new wave of quantum foundations. The ebook is directed at researchers in physics, machine technological know-how, and arithmetic and will be acceptable because the foundation of a graduate path in Quantum Foundations.
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16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. G. Birkhoff, J. von Neumann, Ann. , second series 37, 823–843 (1936) C. Piron, Helv. Phys. P. Solèr, Commun. S. Holland, Bull. Am. Math. Soc. G. Stueckelberg, Helv. Phys. G. Stueckelberg, Helv. Phys. Acta 33, 727 (1960) P. J. Maczynski, J. Math. Phys. 28, 1764–1769 (1987) H. Araki, Commun. Math. Phys. 75, 1 (1980) S. Bergia, F. Cannata, A. Cornia, R. Livi, Found. Phys. K. Wootters, in Complexity, Entropy and the Physics of Information, ed.
Zoller, Phys. Rev. Lett. 78, 390 (1997) 43 Almost Quantum Theory Benjamin Schumacher and Michael D. 1 Motivation The remarkable features of quantum theory are best appreciated by comparing the theory to other possible theories—what Spekkens calls “foil” theories [1]. The most celebrated example of this approach was Bell’s analysis [2], which showed that entangled quantum systems have statistical properties unlike any hypothetical local hidden variable model. More recently, there have been several efforts to give quantum theory an operational axiomatic foundation [3–5].
Since we need to be able to recover our plaintext correctly, it is appropriate to require as an axiom that c be a one-to-one function, so that each letter in the ciphertext can be decoded in only one way. Since A is finite, all one-to-one functions on A are permutations. This means that the generalization from transpositions to permutations already encompasses all reasonable substitution ciphers (as characterized by our axiom). To generalize further, we must extend the idea of a cipher beyond simple letter substitutions.