Quantum injectivity of g-frames in finite dimensions

Abstract

Some recent references have considered quantum detection problems in discrete and continuous frames. This paper examines the quantum detection problem with g-frame in finite dimensions. We will discuss two issues related to the problem at hand: the quantum injectivity problem and the solvability of the quantum state estimation problem. This work addresses the quantum detection problem in a broader context and provides multiple descriptions of quantum injective g-frames. Specifically, we also offer a quantitative stability outcome for g-frames.

Keywords:

• Quantum detection
• quantum injectivity
• g-frames
• operator-valued measure

Mathematics Subject Classification (2010):

• 42C15
• 46C05
• 47B15
• 47L90

Authors' contributions

All authors contributed equally and significantly in writing this article.

Disclosure statement

The authors declare that they have no conflicts of interest.

Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant number 11671201].