On distinguishability distillation and dilution exponents

on distinguishability versus indistinguishability

The following comments are from the book Quantum Mechanics by Claude CohenTannoudji, Bernard Diu, and Franck Laloë. Identical particles: definition Two particles are said to be identical if all their intrinsic properties (mass, spin, charge, etc.) are exactly the same: no experiment can distinguish one from the other. Thus, all electrons in the universe are identical, as are all the protons and...

Tight Bounds on Profile Redundancy and Distinguishability

The minimax KL-divergence of any distribution from all distributions in a collection P has several practical implications. In compression, it is called redundancy and represents the least additional number of bits over the entropy needed to encode the output of any distribution in P . In online estimation and learning, it is the lowest expected log-loss regret when guessing a sequence of random...

From Absolute Distinguishability to Positive Distinguishability

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...

Distinguishability Operations and Closures on Regular Languages

In this paper we study the language of the words that, for a given language L, distinguish between pairs of different left-quotients of L. We characterize this distinguishability operation, show that its iteration has always a fixed point, and we generalize this result to operations derived from closure operators and Boolean operators. We give an upper bound for the state complexity of the dist...

Progress on Membrane Distillation and Related Technologies