We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic… (More)

In this paper we do two things. In Section 2 we obtain complementary inequalities. That is, for 0 ≤ r ≤ 1 we obtain upper bounds on Tr[ABA] (in terms of the quantity Tr[ABA]), and lower bounds for r… (More)

We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation EF and the conjugate function E∗ of the entanglement function E(ρ) = S(TrAρ). We then… (More)

We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states σ1, . . . , σr. By splitting up the overall test into multiple binary tests in… (More)

We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.

The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many… (More)

The stabilizer formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of n-qubit systems. That same formalism has important applications in the field… (More)

According to a celebrated result by Löwner, a real-valued function f is operator monotone if and only if its Löwner matrix, which is the matrix of divided differences Lf = ( f(xi)−f(xj) xi−xj )N… (More)

We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms… (More)

In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We… (More)