论文标题
由痕量非刺激图和加性噪声引起的量子单调指标
Quantum monotone metrics induced from trace non-increasing maps and additive noise
论文作者
论文摘要
Petz引入了量子单调指标，并证明具有痕量量子态的量子单调指标以算子单调函数为特征。后来，将它们扩展到单调指标上的一个正算子集，其痕迹并不总是基于完全积极的，痕量保存（CPTP）地图的痕迹。结果表明，这些扩展的单调指标的特征是算子单调函数通过正算子的痕迹连续参数化，并且没有一些理想的特性，例如单调性和相对于正算子的凸性。在本文中，我们介绍了量子单调指标的另一个扩展，该指标具有完全正面的，痕量非进攻（CPTNI）地图和附加噪声的单调性。我们证明，我们的扩展单调指标只能通过静态算子单调函数来表征，而不假设指标的连续性。我们表明，单调指标具有一些自然属性，例如直接总和，凸度和单调性相对于正运算符。
Quantum monotone metric was introduced by Petz,and it was proved that quantum monotone metrics on the set of quantum states with trace one were characterized by operator monotone functions. Later, these were extended to monotone metrics on the set of positive operators whose traces are not always one based on completely positive, trace preserving (CPTP) maps. It was shown that these extended monotone metrics were characterized by operator monotone functions continuously parameterized by traces of positive operators,and did not have some ideal properties such as monotonicity and convexity with respect to the positive operators. In this paper, we introduce another extension of quantum monotone metrics which have monotonicity under completely positive, trace non-increasing (CPTNI) maps and additive noise. We prove that our extended monotone metrics can be characterized only by static operator monotone functions from few assumptions without assuming continuities of metrics. We show that our monotone metrics have some natural properties such as additivity of direct sum, convexity and monotonicity with respect to positive operators.
