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Decoherence-Insensitive Quantum Communication by Optimal $C^{ast }$-Encoding

机译:通过最佳$ C ^ {ast} $-编码的去相干不敏感量子通信

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摘要

The central issue in this paper is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this purpose, we incorporate redundancy by mapping a given initial quantum state to a messenger state on a larger dimensional Hilbert space via a $C^{ast }$-algebra embedding. Our noise model for the transmission is a phase damping channel which admits a noiseless subsystem or decoherence-free subspace. More precisely, the transmission channel is obtained from convex combinations of a set of lowest rank yeso measurements that leave a component of the messenger state unchanged. The objective of our encoding is to distribute quantum information optimally across the noise-susceptible component of the transmission when the noiseless component is not large enough to contain all the quantum information to be transmitted. We derive simple geometric conditions for optimal encoding and construct examples of such encodings.
机译:本文的中心问题是要以这样一种方式传输量子态,即在发生一些退相干之后,可以通过适当的解码操作来恢复大多数信息。为此,我们通过$ C ^ {ast} $-代数嵌入将给定的初始量子态映射到较大维希尔伯特空间上的信使状态,从而引入冗余。我们用于传输的噪声模型是一个相位阻尼通道,该通道允许一个无噪声的子系统或无相干的子空间。更精确地,传输信道是从一组最低等级的是/否测量的凸组合获得的,这些测量使信使状态的分量保持不变。我们的编码目标是在无噪声分量不足以容纳所有要传输的量子信息时,在传输的噪声敏感分量之间最佳地分配量子信息。我们得出用于最佳编码的简单几何条件,并构建此类编码的示例。

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