Maximum Dimension of Subspaces with No Product Basis

Abstract

Let n ≥ 2 and d 1 , . . . , d n ≥ 2 be integers, and F be a field. A vectorA basis composed of product vectors is called a product basis. In this paper, we show that the maximum dimension of subspaces offor some n 1 and n 2 . When F = C, this result is related to the maximum number of simultaneously distinguishable states in general probabilistic theories (GPTs).