A violation of the uncertainty principle implies a violation of the second law of thermodynamics

Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? We give a strong argument that justifies uncertainty relations in quantum theory by showing that violating them implies that it is also possible to violate the second law of thermodynamics. More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.Comment: 8 pages, revte

Fine-grained uncertainty relation and nonlocality of tripartite systems

The upper bound of the fine-grained uncertainty relation is different for classical physics, quantum physics and no-signaling theories with maximal nonlocality (supper quantum correlation), as was shown in the case of bipartite systems [J. Oppenheim and S. Wehner, Science 330, 1072 (2010)]. Here, we extend the fine-grained uncertainty relation to the case of tripartite systems. We show that the fine-grained uncertainty relation determines the nonlocality of tripartite systems as manifested by the Svetlichny inequality, discriminating between classical physics, quantum physics and super quantum correlations.Comment: 4 page

Fine-grained EPR-steering inequalities

We derive a new steering inequality based on a fine-grained uncertainty relation to capture EPR-steering for bipartite systems. Our steering inequality improves over previously known ones since it can experimentally detect all steerable two-qubit Werner state with only two measurement settings on each side. According to our inequality, pure entangle states are maximally steerable. Moreover, by slightly changing the setting, we can express the amount of violation of our inequality as a function of their violation of the CHSH inequality. Finally, we prove that the amount of violation of our steering inequality is, up to a constant factor, a lower bound on the key rate of a one-sided device independent quantum key distribution protocol secure against individual attacks. To show this result, we first derive a monogamy relation for our steering inequality.Comment: 5 pages, Accepted for publication as a Rapid Communication in Physical Review