Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination (Q2928100)

In this 39-page multi-mathematical paper the authors have considered in a communicative scenario the multiple hypothesis testing problem for symmetric quantum state discrimination between \(r\) distinct states. After a detailed introduction a summary of the necessary preliminaries and review of many known related results are given in the second section. In the third section the upper bounds from suboptimal measurements are discussed while the fourth section deals with binary state discrimination problem with the fifth section treating in detail the dichotomic discrimination questions. Nussbaum's mixed exponents approach is discussed next whereas the final seventh section is devoted to asymptotics: The Chernoff bound.NEWLINENEWLINE There are 42 references, 5 appendices (with 25 equations) which are quite explanatory, 78 main equations, 14 theorems with proof, 6 conjectures, 9 remarks, 8 lemmas, 1 proposition and 2 corollaries in all.NEWLINENEWLINE Studies in probabilistic approaches and behaviour of anything and everything in nature are extremely important. The paper under review is an eloquent example of this fact.NEWLINENEWLINE Altogether the results are quite interesting and useful.