Construction of channels which in every dimension anti-degrade the depolarizing channel
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916014262845440 |
|---|---|
| author | Roofeh, Shayan Karimipour, Vahid |
| author_facet | Roofeh, Shayan Karimipour, Vahid |
| contents | We consider the depolarizing channel in $d$ dimension defined as $D_x(ρ)=(1-x)ρ+x\: \textit{tr}(ρ) \frac{I}{d}$, and explicitly find a quantum channel ${\cal N}_x$ which anti-degrades this, when $x\geq\frac{1}{2}$. This proves that the depolarizing channel $D_x$ has zero capacity when $x\geq\frac{1}{2}$. As a corollary, this implies that any quantum channel when contaminated by white noise stronger than this value loses its capacity completely. Although by arguments based on symmetric-extendibiliy of the Choi matrix, it is known that the channel is anti-degradable when $x\geq \frac{d}{2(d+1)}$, the explicit form of the anti-degrading channel in this larger interval is not known. We also calculate in closed form the capacity of the complenetary channel ${\cal D}_x^c$ in the region $x\geq \frac{1}{2}$. This adds to the existing list of quantum channels for which the quantum capacity has been calculated in closed form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05733 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of channels which in every dimension anti-degrade the depolarizing channel Roofeh, Shayan Karimipour, Vahid Quantum Physics We consider the depolarizing channel in $d$ dimension defined as $D_x(ρ)=(1-x)ρ+x\: \textit{tr}(ρ) \frac{I}{d}$, and explicitly find a quantum channel ${\cal N}_x$ which anti-degrades this, when $x\geq\frac{1}{2}$. This proves that the depolarizing channel $D_x$ has zero capacity when $x\geq\frac{1}{2}$. As a corollary, this implies that any quantum channel when contaminated by white noise stronger than this value loses its capacity completely. Although by arguments based on symmetric-extendibiliy of the Choi matrix, it is known that the channel is anti-degradable when $x\geq \frac{d}{2(d+1)}$, the explicit form of the anti-degrading channel in this larger interval is not known. We also calculate in closed form the capacity of the complenetary channel ${\cal D}_x^c$ in the region $x\geq \frac{1}{2}$. This adds to the existing list of quantum channels for which the quantum capacity has been calculated in closed form. |
| title | Construction of channels which in every dimension anti-degrade the depolarizing channel |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.05733 |