Quantum injectivity of continuous g-frames

Abstract

A quantum injective frame is a frame that can be used to distinguish quantum systems by measuring density operators.
The quantum detection problem aims to characterize all such frames. Recently, there has been significant attention on the problem of quantum detection in both finite and infinite dimensional Hilbert spaces, for both continuous and discrete frames. This paper aims to present various characterizations for injective continuous g-frames.
The work solves the quantum detection problem in a more general context and provides characterizations for a larger class of injective continuous g-frames.