# Finite Operator-Valued Frames - Mathematics > Functional Analysis

Abstract: Operator-valued frames are natural generalization of frames that have beenused in quantum computing, packets encoding, etc. In this paper, we focus ondeveloping the theory about operator-valued frames for finite Hilbert spaces.Some results concerning dilation, alternate dual, and existence ofoperator-valued frames are given. Then we characterize the optimaloperator-valued frames under the case which one packet of data is lost intransmission. At last we construct the operator-valued frames $\{V j\} {j=1}^m$with given frame operator $S$ and satisfying $V jV j^*=\alpha jI$, where$\alpha j-s$ are positive numbers.

Author: Bin Meng

Source: https://arxiv.org/