Abstract
The quantum detection problem was considered in some recent references for both discrete and continuous frames. The purpose of this paper is to presenting several versions of characterizations for \({\mathcal {S}}_{p}\)-injective continuous frames in terms of discrete representations of continuous frames. This work answers the quantum detection problem in a more general setting and gives the characterizations for a larger class of injective continuous frames. With the help of these characterizations, we obtain some concrete examples of injective continuous frames. Moreover, the stability of \({\mathcal {S}}_{p}\)-injective continuous frames will be addressed.
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The authors wish to thank the anonymous reviewers for their valuable comments and suggestions that have improved the presentation of this paper.
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This work was supported by National Natural Science Foundation of China (Grant numbers 11671201 and 11771379).
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Hong, G., Li, P. On the Continuous Frame Quantum Detection Problem. Results Math 78, 64 (2023). https://doi.org/10.1007/s00025-023-01839-0
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DOI: https://doi.org/10.1007/s00025-023-01839-0