Abstract-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 nonlocality 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.

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This paper proposes a simple voting protocol based on quantum blockchain. Despite being simple, our voting protocol is anonymous, binding, non-reusable, verifiable, eligible, fair and self-tallying. Our protocol is also realizable by the current technology.Keywords electronic voting · quantum computation · blockchain 1. Anonymity. Only the voter knows how he or she votes.

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent the same quantum evolution or quantum state. We show that the stabilizer ZX-calculus can be simplified, removing unnecessary equations while keeping only the essential axioms which potentially capture fundamental structures of quantum mechanics. We thus give a significantly smaller set of axioms and prove that meta-rules like 'colour symmetry' and 'upside-down symmetry', which were considered as axioms in previous versions of the language, can in fact be derived. In particular, we show that the additional symbol and one of the rules which had been recently introduced to keep track of scalars (diagrams with no inputs or outputs) are not necessary.

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