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Hierarchical axioms for quantum mechanics

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Abstract

The origin of nonclassicality in quantum mechanics (QM) has been investigated recently by a number of authors with a view to identifying axioms that would single out quantum mechanics as a special theory within a broader framework such as convex operational theories. In these studies, the axioms tend to be logically unconnected in the sense that no specific ordering of the axioms is implied. Here, we identify a hierarchy of five nonclassical features that separate QM from a classical theory. By hierarchy is meant an axiomatic scheme where the succeeding axioms can be regarded as superstructure built on top of the structure provided by the preceding axioms. In a sense, the latter are necessary, but not sufficient, for the succeeding axioms. In our scheme, the axioms briefly are: (Q1) incompatibility and uncertainty; (Q2) contextuality; (Q3) entanglement; (Q4) nonlocality and (Q5) indistinguishability of identical particles. Such a hierarchy isn’t obvious when viewed from within the quantum mechanical framework, but, from the perspective of generalized probability theories (GPTs), relevant toy GPTs are introduced at each layer when useful to illustrate the action of the nonclassical features associated with the particular layer.

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Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology, Madras, Chennai, 600036, India

    S. Aravinda

  2. Jaypee Institute of Information Technology, A10, Sector 62, Noida, 201309, India

    Anirban Pathak

  3. Poornaprajna Institute of Scientific Research, Bangalore, Karnataka, India

    R. Srikanth

Authors
  1. S. Aravinda
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  2. Anirban Pathak
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  3. R. Srikanth
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Correspondence to Anirban Pathak.

Additional information

Contribution to the Topical Issue “Quantum Correlations”, edited by Marco Genovese, Vahid Karimipour, Sergei Kulik, and Olivier Pfister.

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Aravinda, S., Pathak, A. & Srikanth, R. Hierarchical axioms for quantum mechanics. Eur. Phys. J. D 73, 207 (2019). https://doi.org/10.1140/epjd/e2019-90452-2

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