Abstract
Within the physical constraints of general quantum resource theories, an important job is to study the approximate or probabilistic state conversion. Recently, Kondra et al. had investigated the intermediate regime between probabilistic and approximate transformations, and provided bounds on the fidelity and the probability of state conversion. In this paper, we obtain lower bounds for the fidelity and the probability by adding an fidelity ratio depending on the conversion fidelity between the original state and the optimal state from the resource robustness or some pointed fidelity. We conclude that our upper bounds will be tightened with respect to that of Kondra et al. in all quantum resource theories.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China, Grant Nos. 61771294, 61972235.
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Zuo, HX., Liu, F. Tightening Upper Bounds for Approximate State Conversion. Int J Theor Phys 61, 204 (2022). https://doi.org/10.1007/s10773-022-05172-0
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DOI: https://doi.org/10.1007/s10773-022-05172-0