论文标题
最接近可分离状态时通过准搭配熵进行测量
Closest separable state when measured by a quasi-relative entropy
论文作者
论文摘要
众所周知，对于纯状态，纠缠的相对熵等于还原熵，并且最接近的可分离状态也明确已知。根据最近的结果，Renyi相对熵也相同。我们向纠缠的准搭配熵提出了相同的问题，这是定义为可分离状态集的最小距离，当距离通过准轴向熵测量时。首先，我们考虑一个最大的纠缠状态，并表明任何准搭配性熵的最接近分离状态与纠缠的相对熵相同。然后，我们表明这也适用于某些类别的功能和任何纯净的状态。最后，我们考虑了两个Qubit系统和大量运算符凸功能的任何纯状态。对于这些，我们发现最接近的可分离状态，这可能与纠缠的相对熵可能不同。
It is well known that for pure states the relative entropy of entanglement is equal to the reduced entropy, and the closest separable state is explicitly known as well. The same holds for Renyi relative entropy per recent results. We ask the same question for a quasi-relative entropy of entanglement, which is an entanglement measure defined as the minimum distance to the set of separable state, when the distance is measured by the quasi-relative entropy. First, we consider a maximally entangled state, and show that the closest separable state is the same for any quasi-relative entropy as for the relative entropy of entanglement. Then, we show that this also holds for a certain class of functions and any pure state. And at last, we consider any pure state on two qubit systems and a large class of operator convex function. For these, we find the closest separable state, which may not be the same one as for the relative entropy of entanglement.
