标题： 零错误可纠性与 twirling 信道的相位 retrievability 显示英文标题

标题： Zero Error Correctibility and Phase Retrievability for Twirling Channels

摘要： 一个自旋通道是一种由连续的酉表示 $\pi = \sum_{i}^{\oplus} m_i\pi_i$ 引发的量子信道，其中 $\pi_i$ 是不等价的不可约表示。 受最近关于 $\Phi_{\pi}$ 的混合幺正秩最小值的研究工作 \cite{Twirling} 的启发，我们探讨了量子信道 $\Phi_{\pi}$ 的独立数、零误差容量、量子码、正交指数和相位可恢复性与其不可约表示的重数 $m_i$ 和不可约表示的维数 $\dim H_{\pi_i}$ 之间的联系。 特别是，我们证明了图$\Phi_{\pi}$的独立数是多重性的和，图$\Phi_{\pi}$的正交指数正好是那些表示维数的和，并且零错误容量等于$\log (\sum_{i=1}^{d}m_i)$。 我们还给出了$C^n$的相位可恢复框架的极小长度的下界来表示相位可恢复性。 显示英文摘要

摘要： A twirling channel is a quantum channel induced by a continuous unitary representation $\pi = \sum_{i}^{\oplus} m_i\pi_i$, where $\pi_i$ are inequivalent irreducible representations. Motivated by a recent work \cite{Twirling} on minimal mixed unitary rank of $\Phi_{\pi}$, we explore the connections of the independence number, zero error capacity, quantum codes, orthogonality index and phase retrievability of the quantum channel $\Phi_{\pi}$ with the irreducible representation multiplicities $m_i$, the irreducible representation dimensions $\dim H_{\pi_i}$. In particular we show that the independence number of $\Phi_{\pi}$ is the sum of the multiplicities, the orthogonal index of $\Phi_{\pi}$ is exactly the sum of those representation dimensions, and the zero-error capacity is equal to $\log (\sum_{i=1}^{d}m_i)$. We also present a lower bound for the phase retrievability in terms of the minimal length of phase retrievable frames for $C^n$.