We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt–rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidt–rank width to the optimal description of states in terms of tree tensor networks and show that an...

Nonpremixed jet flames of dimethyl ether (DME) were studied both experimentally and theoretically to investigate flame liftoff near unity Schmidt number. It was found experimentally that although the DME nonpremixed flames have a Schmidt number larger than unity it cannot be lifted directly by increasing the flow rate. Lifted flames can only be established by igniting the mixture in a narrow re...

In this letter, the spectrum of high Schmidt number passive scalar in forced homogeneous isotropic turbulence is studied through direct numerical simulations. A hybrid spectral-particle method is used with a finer resolution of the scalar than of the momentum and large time-steps. This approach enables to perform a systematic analysis over a wide range of Schmidt numbers. Our results recover th...

This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...