Quantum Injectivity of Frames in Quaternionic Hilbert Spaces

Zhenheng Xu, Guoqing Hong (), Zuhua Guo and Jianxia Zhang
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Zhenheng Xu: School of Vehicle and Traffic Engineering, Henan Institute of Technology, Xinxiang 453003, China
Guoqing Hong: School of Science, Henan Institute of Technology, Xinxiang 453003, China
Zuhua Guo: School of Computer Science and Technology, Henan Institute of Technology, Xinxiang 453003, China
Jianxia Zhang: School of Intelligent Engineering, Henan Institute of Technology, Xinxiang 453003, China

Mathematics, 2024, vol. 12, issue 14, 1-12

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.

Keywords: frame; quaternionic Hilbert space; quantum detection; quantum injectivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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