A new estimation of the quantum Chernoff bound
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912297833725952 |
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| author | Kian, Mohsen Dinh, Trung Hoa Moslehian, Mohammad Sal Osaka, Hiroyuki |
| author_facet | Kian, Mohsen Dinh, Trung Hoa Moslehian, Mohammad Sal Osaka, Hiroyuki |
| contents | Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*}
\mathrm{tr}(A+B) - \mathrm{tr}|A-B|\leq 2\, \mathrm{tr}\big(f(A)g(B)\big) \end{align*} holds for every positive-valued matrix monotone function $f$, where $g(x)=x/f(x)$, and all positive definite matrices $A$ and $B$.
In this paper, we introduce a new class of functions that satisfy the above inequality. As a consequence, we derive a novel estimation of the quantum Chernoff bound. Additionally, we characterize matrix decreasing functions and establish matrix Powers-Störmer type inequalities for perspective functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07818 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new estimation of the quantum Chernoff bound Kian, Mohsen Dinh, Trung Hoa Moslehian, Mohammad Sal Osaka, Hiroyuki Quantum Physics Functional Analysis 46N50, 15A15, 46L30 Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathrm{tr}|A-B|\leq 2\, \mathrm{tr}\big(f(A)g(B)\big) \end{align*} holds for every positive-valued matrix monotone function $f$, where $g(x)=x/f(x)$, and all positive definite matrices $A$ and $B$. In this paper, we introduce a new class of functions that satisfy the above inequality. As a consequence, we derive a novel estimation of the quantum Chernoff bound. Additionally, we characterize matrix decreasing functions and establish matrix Powers-Störmer type inequalities for perspective functions. |
| title | A new estimation of the quantum Chernoff bound |
| topic | Quantum Physics Functional Analysis 46N50, 15A15, 46L30 |
| url | https://arxiv.org/abs/2302.07818 |