基于量子信道的量子和经典信息识别
Quantum and Classical Message Identification via Quantum Channels
摘要：
我们讨论的概念，通过一般的量子信道的Ahlswede和Dueck的意义上的消息识别，扩展经典信道的调查，经典量子（CQ）信道和“量子指纹”的初步工作。我们证明，离散无记忆量子信道对经典信息的识别能力可以大于传输能力;这与之前考虑的所有模型相反，其中它等于常见的随机性能力（在我们的情况下等于传输容量）：特别地，对于无噪声量子比特，我们表明识别容量为2，而传输和公共随机容量为1。然后我们转向量子信息识别的自然概念（即量子态的“指纹”概念）。这比它的经典对应物更接近于量子信息传输（首先，与经典识别的双指数相比，代码长度仅呈指数增长）。事实上，我们展示了这个问题如何与可见量子编码有很好的联系。令人惊讶的是，对于无噪声量子比特通道，这个容量原来是2：换句话说，可以将两个量子比特压缩成一个，这是最佳的。然而，在一般情况下，我们推测量子识别能力是不同于经典的识别能力。
英文摘要：
We discuss concepts of message identification in the sense of Ahlswede and Dueck via general quantum channels, extending investigations for classical channels, initial work for classical-quantum (cq) channels and "quantum fingerprinting". We show that the identification capacity of a discrete memoryless quantum channel for classical information can be larger than that for transmission; this is in contrast to all previously considered models, where it turns out to equal the common randomness capacity (equals transmission capacity in our case): in particular, for a noiseless qubit, we show the identification capacity to be 2, while transmission and common randomness capacity are 1. Then we turn to a natural concept of identification of quantum messages (i.e. a notion of "fingerprint" for quantum states). This is much closer to quantum information transmission than its classical counterpart (for one thing, the code length grows only exponentially, compared to double exponentially for classical identification). Indeed, we show how the problem exhibits a nice connection to visible quantum coding. Astonishingly, for the noiseless qubit channel this capacity turns out to be 2: in other words, one can compress two qubits into one and this is optimal. In general however, we conjecture quantum identification capacity to be different from classical identification capacity.
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