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)

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)

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)

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)

Partitions can be graphically represented by Young frames, which are Young tableaux with empty boxes. The i-th part λi corresponds to the i-th row of the frame, consisting of λi boxes. Conversely,… (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.

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)

Murthy and Sethi (Sankhya Ser B 27, 201–210 (1965)) gave a sharp upper bound on the variance of a real random variable in terms of the range of values of that variable. We generalise this bound to… (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)