标题： 在嘈杂网络中无需长时间量子存储的长距离量子通信 显示英文标题

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

摘要： 远距离纠缠共享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间共享爱因斯坦-波多尔斯基-罗森（EPR）对的网络。 在Perseguers等人[Phys. Rev. A 78, 062324 (2008)]中，作者提出了在维度为$D$存储量子信息与在维度为$D+1$的网络中传输量子信息之间的一个重要同构关系。 我们证明了即使考虑到编码和解码过程会受到错误影响，在噪声二维（2D）网络中仍然可以实现长距离纠缠。对于三维（3D）网络，我们提出了一种基于二维Kitaev拓扑量子存储器的简单编码和解码方案。 我们的方法构成了一种替代的状态注入方案，可用于二维Kitaev码上的通用量子计算。我们展示了该编码方案等价于通过存在于剩余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。 我们给出了编码和解码程序保真度的解析下界，主要工具是时空晶格上的一种修正度量，在第一个和最后一个时间切片处偏离出租车度量。 显示英文摘要

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.