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arXiv quant-ph/0307104quant-ph
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随机化量子态的构造与应用

Randomizing quantum states: Constructions and applications

Patrick Hayden, Debbie Leung, Peter W. Shor, Andreas Winter

摘要:

已知在d维中构造完全安全的私有量子信道需要发送方和接收方之间的2log d个共享随机密钥比特。我们表明,如果只需要接近完美的安全性,密钥的大小可以减少了两倍。更具体地说,我们证明了存在一组近似为d log d的幺正算符,它们对每个输入纯态的平均影响几乎是完全随机化的,而完全随机化需要d^2个算符。除了私有量子信道之外,这种构造的变体可以应用于量子信息处理中的许多其他任务。例如,我们表明,它可以用来构建LOCC数据隐藏方案的位和量子位,比任何其他已知的更有效,允许大约log d量子位隐藏在2 log d量子位。该方法也可以用来展示存在的量子态与锁定的经典相关性,一个任意大的放大的相关性被完成发送一个可忽略的小经典密钥。我们的结构还提供了一种远程制备任意d维纯量子态的方法,使用约log d比特的通信和log d ebits的纠缠的基本积木。

英文摘要:

The construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver. We show that if only near-perfect security is required, the size of the key can be reduced by a factor of two. More specifically, we show that there exists a set of roughly d log d unitary operators whose average effect on every input pure state is almost perfectly randomizing, as compared to the d^2 operators required to randomize perfectly. Aside from the private quantum channel, variations of this construction can be applied to many other tasks in quantum information processing. We show, for instance, that it can be used to construct LOCC data hiding schemes for bits and qubits that are much more efficient than any others known, allowing roughly log d qubits to be hidden in 2 log d qubits. The method can also be used to exhibit the existence of quantum states with locked classical correlations, an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key. Our construction also provides the basic building block for a method of remotely preparing arbitrary d-dimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement.

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。

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