Non-Locality, Complementarity and Cosmology

Menas C. Kafatos, R. Nadeau

Walter von Lucadou

Natalia K. Kisel

The paper is devoted to the research of the role of the anthropal cosmological principle (ACP) in the formation of the post-non-classical scientific rationality. The comparative analysis of ACP and the principles of complementarity and observability in non-classical science has been made, the methodological significance of ACP in the formation of the communicative strategy of post-non-classical science has been found.

Bob Coecke, Ross Duncan, Aleks Kissinger +1 more

Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here. Our derivation of the fact that strong complementarity is a necessary condition for a Mermin scenario provides a crisp operational interpretation for strong complementarity. We also provide a complete classification of strongly complementary observables for quantum theory, something which has not yet been achieved for ordinary complementarity. Since our main results are expressed in the (diagrammatic) language of dagger-compact categories, they can be applied outside of quantum theory, in any setting which supports the purely algebraic notion of strongly complementary observables. We have therefore introduced a method for discussing non-locality in a wide variety of models in addition to quantum theory. The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights. In particular, the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect. In other words, we depict non-locality.

P. Achuthan, Narayanankutty Karuppath

Liang-Liang Sun, Sixia Yu, Zeng‐Bing Chen

We propose an uncertainty-complementarity balance relation and build quantitative connections among non-locality, complementarity, and uncertainty. Our balance relation, which is formulated in a theory-independent manner, states that for two measurements performed sequentially, the complementarity demonstrated in the first measurement in terms of disturbance is no greater than the uncertainty of the first measurement. Quantum theory respects our balance relation, from which the Tsirelson bound can be derived, up to an inessential assumption. In the simplest Bell scenario, we show that the bound of Clauser-Horne-Shimony-Holt inequality for a general non-local theory can be expressed as a function of the balance strength, a constance for the given theory. As an application, we derive the balance strength as well as the nonlocal bound of Popescu-Rohrlich box. Our results shed light on quantitative connections among three fundamental concepts, i.e., uncertainty, complementarity and non-locality.