Maps on positive definite operators preserving the quantum $$chi _alpha ^2$$χα2-divergence
Maps on positive definite operators preserving the quantum $$chi _alpha ^2$$χα2-divergence
复制标题
保留量子 $$chi _alpha ^2$$χα2-散度的正定算子上的映射
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
N. Wong
中科院分区：
文献类型：
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作者：
Hong;G. P. Gehér;Chih;L. Molnár;Dániel Virosztek;N. Wong
我们描述了作用于有限且至少二维复希尔伯特空间的正定算子锥体上的所有双射映射的结构，该空间保留了 [0,1]$$αε[0,1] 中某些 $$alpha 的量子 $$chi _alpha ^2$$χα2-散度。我们证明任何这样的变换都必然由酉算子或反酉算子来实现。关于正半定算子锥体上的映射以及所有密度算子集合上的映射也得出了类似的结果。
We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum $$chi _alpha ^2$$χα2-divergence for some $$alpha in [0,1]$$α∈[0,1]. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.