Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
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DOI：
10.1007/s11511-014-0113-6
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发表时间：
2014-06-01
期刊：
影响因子：
3.7
通讯作者：
Solovej, Jan Philip
中科院分区：
文献类型：
--
作者：
Lieb, Elliott H.;Solovej, Jan Philip
Wehrl使用Glauber相干态定义了从量子密度矩阵到经典相空间密度的映射，并推测对于Glauber相干态，当密度矩阵等于投射到相干态时，将出现最小经典熵。这是由Lieb在1978年证明的，他还将这一猜想推广到每个角动量J的Bloch Su(2)自旋相干态。我们还回顾了1991年我们将Wehrl映射扩展到从J到W的量子通道，对应于经典密度的Wehrl映射。这些通道后来被认为是最佳的量子克隆通道。对于每个J，我们证明了对于J相干态，通道的最小输出熵出现。我们还证明了Glauber和Bloch相干态都最小化了任何凹泛函，而不仅仅是熵。
Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum J. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum channel from J to with corresponding to the Wehrl map to classical densities. These channels were later recognized as the optimal quantum cloning channels. For each J and we show that the minimal output entropy for the channels occurs for a J coherent state. We also show that coherent states both Glauber and Bloch minimize any concave functional, not just entropy.