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...

A statistical distinguishability based on relative entropy characterizes the fitness of quantum states for phase estimation. This criterion is employed in the context of a Mach-Zehnder interferometer and used to interpolate between two regimes of local and global phase distinguishability. The scaling of distinguishability in these regimes with photon number is explored for various quantum state...

We study methods of converting algorithms that distinguish pairs of distributions with a gap that has an absolute value that is noticeable into corresponding algorithms in which the gap is always positive (and noticeable). Our focus is on designing algorithms that, in addition to the tested string, obtain a fixed number of samples from each distribution. Needless to say, such algorithms can not...

We aim at formalizing the notion of distin-guishability. Intuitively, distinguishability refers to the transitions between diierent levels of detail with which diierent agents refer to the same objects. We frame our work within the notion of contexts, as a way to provide agents with local reasoning capabilities and to express their compati-bilities. We believe distinguishability plays an import...

Quantum interference of two independent particles in pure quantum states is fully described by the particles' distinguishability: the closer the particles are to being identical, the higher the degree of quantum interference. When more than two particles are involved, the situation becomes more complex and interference capability extends beyond pairwise distinguishability, taking on a surprisin...

This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an id...

In this Letter we present a necessary condition for distinguishability of multi-partite orthogonal quantum states by local operations and classical communication. With this condition one can discuss the distinguishability of orthogonal states further. We also present a necessary condition for distinguishability of bipartite orthogonal quantum states by local operations and classical, which is s...

Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the context. In this research, the essence of an algebraic semantics that can deal with all possible concepts of distinguishability over similarity spaces is pro...