霍夫曼编码的量子模拟
A quantum analog of Huffman coding
摘要：
我们分析了量子情况下的霍夫曼编码的推广。特别是，我们注意到使用瞬时码进行量子通信的各种困难。然而，对于量子信息的存储，我们已经成功地构建了一个哈夫曼编码启发的量子方案。通过量子门阵列的大规模并行实现，可以使N个量子信号的编码和解码过程中的计算步骤的数量具有多对数深度。这是比较所需的O（N^3）计算步骤的顺序实现由克里夫和Diplenenzo著名的量子无噪声分组编码方案的舒马赫。我们还表明，O（N^2（log N）^a）的计算步骤需要使用另一个霍夫曼编码启发方案的量子信息的通信发送方必须解开她的编码设备之前，接收方可以执行任何测量他的信号。
英文摘要：
We analyze a generalization of Huffman coding to the quantum case. In particular, we notice various difficulties in using instantaneous codes for quantum communication. Nevertheless, for the storage of quantum information, we have succeeded in constructing a Huffman-coding inspired quantum scheme. The number of computational steps in the encoding and decoding processes of N quantum signals can be made to be of polylogarithmic depth by a massively parallel implementation of a quantum gate array. This is to be compared with the O (N^3) computational steps required in the sequential implementation by Cleve and DiVincenzo of the well-known quantum noiseless block coding scheme of Schumacher. We also show that O(N^2(log N)^a) computational steps are needed for the communication of quantum information using another Huffman-coding inspired scheme where the sender must disentangle her encoding device before the receiver can perform any measurements on his signals.
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