Phase-retrievable operator-valued frames and representations of quantum channels
Phase-retrievable operator-valued frames and representations of quantum channels
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DOI：
10.1016/j.laa.2019.05.017
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发表时间：
2019-10
影响因子：
1.1
通讯作者：
D. Han;Ted Juste
中科院分区：
文献类型：
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作者：
D. Han;Ted Juste
我们研究了相位可恢复（不一定自伴随）算子值帧、射影群表示帧和量子信道表示之间的一些联系。我们首先给出了作用于有限维和无限维Hilbert空间的一般算子系统的相位可恢复框架的一些特征，推广了对向量值框架、融合框架和厄米矩阵框架的已知结果。对于有限群的不可约射影酉表示，图像系统是相位可自动恢复的，并且是一个点紧算子值帧。我们将这一概念推广到更一般的算子值坐标系，并证明了点紧算子值坐标系就是与算子值紧坐标系完全等价的紧坐标系。对于表示量子信道的算子系统，我们证明了系统的相位可恢复性与量子信道表示的选择无关。
We examine some connections among phase-retrievable (not necessarily self-adjoint) operator-valued frames, projective group representation frames and representations of quantum channels. We first present some characterizations of phase-retrievable frames for general operator systems acting on both finite and infinite dimensional Hilbert spaces, which generalize the known results for vector-valued frames, fusion frames and frames of Hermitian matrices. For an irreducible projective unitary representation of a finite group, the image system is automatically phase-retrievable and, moreover, it is a point-wisely tight operator-valued frames. We generalize this notion to more general operator-valued frames, and prove that point-wise tight operator-valued frames are exactly the ones that are right equivalent to operator-valued tight frames. For an operator system that represent a quantum channel, we show that phase-retrievability of the system is independent of the choices of the representations of the quantum channel.