摘要
Operator-valued frames are natural generalization of frames that have been used in many applied areas such as quantum computing, packets encoding and sensor networks. We focus on developing the theory about operator-valued frame generators for projective unitary representations of finite or countable groups which can be viewed as the theory of quantum channels with group structures. We present new results for operator-valued frames concerning (general and structured) dilation property, orthogonal frames, frame representation and dual frames. Our results are complementary to some of the recent work of Kaftal, Larson and Zhang, and in some cases our treatment is more elementary and transparent.
Operator-valued frames are natural generalization of frames that have been used in many applied areas such as quantum computing, packets encoding and sensor networks. We focus on developing the theory about operator-valued frame generators for projective unitary representations of finite or countable groups which can be viewed as the theory of quantum channels with group structures. We present new results for operator- valued frames concerning （general and structured） dilation property, orthogonal frames, frame representation and dual frames. Our results are complementary to some of the recent work of Kaftal, Larson and Zhang, and in some cases our treatment is more elementary and transparent.
基金
supported by Singapore Ministry of Education Academic Research Fund Tier 1 (Grant No. R-146-000-136-112)
National Natural Science Foundation of China (Grant No. 10771101)
US National Science Foundation (Grant No. DMS-1106934)
关键词
量子通道
运营商
结构
价值
框架
传感器网络
量子计算
数据包
operator-valued frames, quantum channels, Parseval duals, projective unitary representation
