Quantum Injectivity of Frames in Quaternionic Hilbert Spaces

Abstract

A quantum injective frame is a frame capable of differentiating states based on their respective frame measurements, whereas the quantum-detection problem associated with frames endeavors to delineate all such frames. In the present paper, the concept of injective frames in infinite dimensional quaternionic Hilbert spaces is introduced. Further, some properties of injective frames such as the invariance of injective frames under invertible operators are discussed and several solutions to the frame quantum-detection problem are given. Finally, by employing operator theory and frames theory in quaternionic Hilbert spaces, some characterizations and classifications of frames for solving the injectivity problem are given.