The quantum speed limit is a fundamental upper bound on the speed of quantum evolution.However, the actualmathematical expression of this fundamental limit depends on the choice of ameasure of distinguishability of quantum states.We show that quantum speed limits are qualitatively governed by the Schatten-p-normof the generator of quantumdynamics. Since computing Schatten-p-norms can bemathemat...

We apply the complex interpolation method to prove that, given two spacesB p0,a;s0 , B (n) p1,b;s1 of n-tuples of operators in the p-Schatten class of a Hilbert space H , endowed with weighted norms associated to positive and invertible operators a and b of B(H) then, the curve of interpolation (B p0,a;s0 , B (n) p1,b;s1 )[t] of the pair is given by the space of n-tuples of operators in the pt-...

We address some theoretical guarantees for Schatten-p quasi-norm minimization (p ∈ (0, 1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measuring operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaran...

Abstract. Generalizing Pisier’s idea, we introduce a Hilbertian matrix cross normed space associated with a pair of symmetric normed ideals. When the two ideals coincide, we show that our construction gives an operator space if and only if the ideal is the Schatten class. In general, a pair of symmetric normed ideals that are not necessarily the Schatten class may give rise to an operator space...

We conjecture the following so-called norm compression inequality for 2×N partitioned block matrices and the Schatten p-norms: for p ≥ 2,