We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, m. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group G, i.e. with a discrete number, {pipe}G{pipe}, of possible noise operators, perfect transmission at a rate m/(m+r) is achieved with an overhead that scales at most as O(d~r) where the number of auxiliary qudits, r, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, m. For certain groups, e.g. cyclic groups, we find that the overhead scales only linearly with the number of group elements {pipe}G{pipe}.
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机译：我们引入了一种新的量子通信协议，用于在集体噪声下传输量子信息。我们的协议以无退相干子空间的方式实现了最佳渐近传输速率，同时可以有效地实现编码和解码操作。编码和解码电路需要多个基本门，这些门与传输的量子数量m成线性比例。我们的编码和解码操作的逻辑深度是恒定的，并且仅取决于所讨论的信道。对于由任意离散组G（即具有离散数量{pipe} G {pipe}）的可能的噪声算子描述的信道，以m /（m + r）的速率实现了完美的传输，而开销最多可扩展为O（d〜r），其中辅助qudits的数量r仅取决于所讨论的组。此外，该开销独立于所发送的qud的数量m。对于某些群体，例如循环组，我们发现开销仅随组元素{pipe} G {pipe}的数量线性增长。
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