A set of orthogonal states in multipartite systems is called to be locally stable if preserve the orthogonality states, only trivial local measurement can performed for each partite. Locally sets are always indistinguishable yielding a form nonlocality which different from Bell-type nonlocality. In this work, we study product with small size. First, give lower bound on size states. It well know...

Consider the class of exp-log constants, which is constructed from the integers using the field operations, exponentiation and logarithm. Let z be such an exp-log constant and let n be its size as an expression. Witness conjectures attempt to give bounds $(n) for the number of decimal digits which need to be evaluated in order to test whether z equals zero. For this purpose, it is convenient to...

The main aim of this paper is to characterize the set of states indistinguishable from a given state of a general nonlinear input-affine control system with complete and smooth vector fields and smooth output functions. For this purpose, we introduce the extended observation space, and show that the set of states indistinguishable from a given state is the intersection of level sets containing ...

In this paper, we introduce and study notions like state-\linebreak distinguishability, input-distinguishability and output completeness of states of a crisp deterministic fuzzy automaton. We show that for each crisp deterministic fuzzy automaton there corresponds a unique (up to isomorphism), equivalent distinguished crisp deterministic fuzzy automaton. Finally, we introduce two axioms related...

One of the fundamental features quantum mechanics is superposition principle, a manifestation which embodied in coherence. Coherence state invariably defined with respect to preferred set pointer states, and there exist coherence measures deterministically as well probabilistically distinguishable sets vectors. Here we study resource theory an arbitrary vectors, that may not even be distinguish...