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Mathematics 2016, 4(3), 52;

Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
Optics and Quantum Information Group, The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai 600113, India
Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, Odisha, India
Author to whom correspondence should be addressed.
Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari
Received: 5 April 2016 / Revised: 28 July 2016 / Accepted: 8 August 2016 / Published: 15 August 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
Full-Text   |   PDF [265 KB, uploaded 15 August 2016]


It has been recently shown that measurement incompatibility and fine grained uncertainty—a particular form of preparation uncertainty relation—are deeply related to the nonlocal feature of quantum mechanics. In particular, the degree of measurement incompatibility in a no-signaling theory determines the bound on the violation of Bell-CHSH inequality, and a similar role is also played by (fine-grained) uncertainty along with steering, a subtle non-local phenomenon. We review these connections, along with comments on the difference in the roles played by measurement incompatibility and uncertainty. We also discuss why the toy model of Spekkens (Phys. Rev. A 75, 032110 (2007)) shows no nonlocal feature even though steering is present in this theory. View Full-Text
Keywords: joint measurability; incompatibility; uncertainty relations joint measurability; incompatibility; uncertainty relations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Kar, G.; Ghosh, S.; Choudhary, S.K.; Banik, M. Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality. Mathematics 2016, 4, 52.

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