arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1202.1016quant-ph
收藏

无长时间量子记忆噪声网络上的长距离量子通信

Long-distance quantum communication over noisy networks without long-time quantum memory

Paweł Mazurek, Andrzej Grudka, Michał Horodecki, Paweł Horodecki, Justyna Łodyga, Łukasz Pankowski, Anna Przysiężna

摘要:

在大距离上共享纠缠的问题对于量子密码学的实现至关重要。一种可能的长距离纠缠共享和量子通信方案利用了节点共享Einstein-Podolsky-Rosen(EPR)对的网络。在Perseguers等人[Phys.Rev.A78,062324(2008)]中,作者提出了在维度$D$中存储量子信息与在$D+1$维网络中传输量子信息之间的重要同构。我们表明,它是可能的,以获得长距离纠缠在嘈杂的二维(2D)网络,即使考虑到编码和解码的状态是暴露于错误。对于3D网络,我们提出了一个简单的编码和解码方案,完全基于2D Kitaev拓扑量子存储器上的综合征测量。我们的程序构成了一个替代方案的状态注入,可用于通用量子计算的二维Kitaev码。结果表明,该编码方案相当于通过存在于网络量子比特中的虚拟EPR对,将状态从特定节点传送到整个二维网络中。我们提出了一个分析下界的编码和解码过程中的保真度,作为我们的主要工具,使用修改后的度量空间-时间格,偏离出租车度量在第一个和最后一个时间片。

英文摘要:

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension $D$ and transmission of quantum information in a $D+1$-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑