Abstract
Motivated by the isomorphic correspondence between quantum channels and their Choi states, we define an entropy function of a quantum channel by the entropy of its Choi state. We show that it satisfies all axioms of the entropy function. We also define the relative entropy of a quantum channel and give the relation between the entropy and the relative entropy of a quantum channel. Moreover, comparing with the entropy of a quantum channel which is defined by Gour and Wilde, we find that the two definitions of the channel entropy are equal for covariant channels. As examples, we compute the entropies of the erasure channel, the d-dimensional depolarizing channel, and a particular kind of Werner–Holevo channels, respectively.
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The datasets analyzed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
This work was supported by Key Research and Development Project of Guang Dong Province under Grant No. 2020B0303300001 and the Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B151 5310016.
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Chu, Y., Huang, F., Li, MX. et al. An entropy function of a quantum channel. Quantum Inf Process 22, 27 (2023). https://doi.org/10.1007/s11128-022-03778-1
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DOI: https://doi.org/10.1007/s11128-022-03778-1