Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond

Roberto Rubboli; Ryuji Takagi; Marco Tomamichel

doi:10.22331/q-2024-10-04-1492

Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond

Roberto Rubboli¹, Ryuji Takagi^2,3, and Marco Tomamichel^1,4

¹Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
²Department of Basic Science, The University of Tokyo, Tokyo 153-8902, Japan
³Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
⁴Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore

Published:	2024-10-04, volume 8, page 1492
Eprint:	arXiv:2307.08258v3
Doi:	https://doi.org/10.22331/q-2024-10-04-1492
Citation:	Quantum 8, 1492 (2024).

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Updated version: The authors have uploaded version v4 of this work to the arXiv which may contain updates or corrections not contained in the published version v3. The authors left the following comment on the arXiv:

v4: Fixed a missing exponent in Section 6, equation 44

Abstract

We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the $\alpha$-$z$ Rényi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation.

► BibTeX data

@article{Rubboli2024mixedstate,
  doi = {10.22331/q-2024-10-04-1492},
  url = {https://doi.org/10.22331/q-2024-10-04-1492},
  title = {Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond},
  author = {Rubboli, Roberto and Takagi, Ryuji and Tomamichel, Marco},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1492},
  month = oct,
  year = {2024}
}

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