Abstract
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.
Highlights
Quantum theory (QT), admittedly the most accurate mathematical description of physical world, is considered as one of the greatest achievements of 20th century science
The paper is organized as follows: In Section 2, we briefly describe the mathematical framework of convex operational theories, the concept of joint measurability, and the concept of fine-grained uncertainty relation
We present an alternative proof of a result by Wolf et al, which shows that measurement incompatibility in QT always results in the violation of the Bell-CHSH inequality [13]
Summary
Quantum theory (QT), admittedly the most accurate mathematical description of physical world, is considered as one of the greatest achievements of 20th century science. The nonlocal strength of quantum correlations is restricted in comparison with other possible correlations compatible with the relativistic causality principle. This restricted behavior is manifested by the amount of optimal violation of the well known Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality [9]. We critically review these connections, which are not limited only to QT, but extend to a much broader framework of convex operational theories. The paper is organized as follows: In Section 2, we briefly describe the mathematical framework of convex operational theories, the concept of joint measurability, and the concept of fine-grained uncertainty relation.
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