The law of large numbers for discrete generalized quantum channels
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914065794727936 |
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| author | Dzhenzher, S. V. Sakbaev, V. Zh. |
| author_facet | Dzhenzher, S. V. Sakbaev, V. Zh. |
| contents | We consider random linear operators $Ω\to \mathcal{L}(\mathcal{T}_p, \mathcal{T}_p)$ acting in a $p$-th Schatten class $\mathcal{T}_p$ in a separable Hilbert space $\mathcal{H}$ for some $1 \leqslant p < \infty$. Such a superoperator is called a pre-channel since it is an extension of a quantum channel to a wider class of operators without requirements of trace-preserving and positivity. Instead of the sum of i.i.d. variables there may be considered the composition of random semigroups $e^{A_i t/n}$ in the Banach space $\mathcal{T}_p$. The law of large numbers is known in the case $p=2$ in the form of the usual law of large numbers for random operators in a Hilbert space. We obtain the law of large numbers for the case $1\leqslant p \leqslant 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The law of large numbers for discrete generalized quantum channels Dzhenzher, S. V. Sakbaev, V. Zh. Functional Analysis Probability We consider random linear operators $Ω\to \mathcal{L}(\mathcal{T}_p, \mathcal{T}_p)$ acting in a $p$-th Schatten class $\mathcal{T}_p$ in a separable Hilbert space $\mathcal{H}$ for some $1 \leqslant p < \infty$. Such a superoperator is called a pre-channel since it is an extension of a quantum channel to a wider class of operators without requirements of trace-preserving and positivity. Instead of the sum of i.i.d. variables there may be considered the composition of random semigroups $e^{A_i t/n}$ in the Banach space $\mathcal{T}_p$. The law of large numbers is known in the case $p=2$ in the form of the usual law of large numbers for random operators in a Hilbert space. We obtain the law of large numbers for the case $1\leqslant p \leqslant 2$. |
| title | The law of large numbers for discrete generalized quantum channels |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2504.10033 |