arXiv quant-ph/02060582002-06quant-ph

量子信道的自适应经典容量或三维对称纯态的信息容量

The Adaptive Classical Capacity of a Quantum Channel, or Information Capacities of Three Symmetric Pure States in Three Dimensions

Peter W. Shor

备注：: 44 pages, 17 figures, minor errors corrected and new Conjecture 1 added (thus renumbering all conjectures); replaced in May, 2003 to correct more minor errors

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摘要：

我们研究了三个实维中三个对称的量子态承载经典信息的能力。根据发送和接收协议中允许的操作，已经定义了几种这样的能力。这些包括C_{1,1}容量和C_{1,infinity}容量，C_{1,1}容量是如果必须对每个接收到的状态使用单独的测量则可实现的容量，C_{1,infinity}容量是如果允许对所有接收到的状态的张量积进行联合测量则可实现的容量。我们发现了量子信道的一种新的经典信息容量--自适应容量C_{1,A}，它严格地介于C_{1,1}和C_{1,infinity}容量之间.自适应能力要求每个信号由单独的装置测量，但是允许分阶段测量这些信号的量子态，其中第一阶段部分地减少它们的量子态，并且其中进一步减少量子态的后续阶段中的测量可以取决于将第一轮测量的结果作为输入的经典计算的结果。

英文摘要：

We investigate the capacity of three symmetric quantum states in three real dimensions to carry classical information. Several such capacities have already been defined, depending on what operations are allowed in the sending and receiving protocols. These include the C_{1,1} capacity, which is the capacity achievable if separate measurements must be used for each of the received states, and the C_{1,infinity} capacity, which is the capacity achievable if joint measurements are allowed on the tensor product of all the received states. We discover a new classical information capacity of quantum channels, the adaptive capacity C_{1,A}, which lies strictly between the C_{1,1} and the C_{1,infinity} capacities. The adaptive capacity requires each of the signals to be measured by a separate apparatus, but allows the quantum states of these signals to be measured in stages, with the first stage partially reducing their quantum states, and where measurements in subsequent stages which further reduce the quantum states may depend on the results of a classical computation taking as input the outcomes of the first round of measurements.

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