Asymmetric quantum cloning in any dimension
Asymmetric quantum cloning in any dimension
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DOI：
10.1080/09500340008244036
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发表时间：
1998-05
影响因子：
1.3
通讯作者：
N. Cerf
中科院分区：
文献类型：
--
作者：
N. Cerf
摘要介绍了一族N维量子态的非对称克隆机。这些机器产生了来自不同海森堡通道的单个状态的两个不完美副本。量子力学所施加的副本的质量之间的权衡是从一个互补性类似于海森堡不确定性原理。更具体地，影响两个副本的误差算子的概率分布是通过傅立叶变换相关的两个函数的平方模。对于各向同性克隆子的特殊情况，导出了一个无克隆不等式，量化了完美克隆的不可能性：如果π a和π B是与两个拷贝相关的去极化分数，则（π1/2 a，π1/2 B）-空间中位于代表接近完美克隆的特定椭圆内的区域是禁止的.更一般地，熵的不可克隆的不确定性关系也进行了讨论。最后，类量子比特的非对称克隆机进行了详细研究，并显示与泡利信道的容量的连接。
Abstract A family of asymmetric cloning machines for N-dimensional quantum states is introduced. These machines produce two imperfect copies of a single state that emerge from non-identical Heisenberg channels. The trade-off between the quality of the copies imposed by quantum mechanics is shown to result from a complementarity akin to the Heisenberg uncertainty principle. More specifically, the probability distributions of the error operators affecting the two copies are the square modulus of two functions related by a Fourier transform. A no-cloning inequality is derived for the special case of isotropic cloners, quantifying the impossibility of perfect cloning: if π a and π b are the depolarizing fractions associated with the two copies, the domain in (π1/2 a , π1/2 b )-space located inside a particular ellipse representing close-to-perfect cloning is forbidden. More generally, an entropic no-cloning uncertainty relation is also discussed. Finally, the class of asymmetric cloning machines for quantum bits is investigated in detail, and a connection with the capacity of the Pauli channel is displayed.