College of Mathematics, Institute of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China.
School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China.
Sci Rep. 2017 Apr 4;7:45598. doi: 10.1038/srep45598.
Coherence is the most fundamental quantum feature in quantum mechanics. For a bipartite quantum state, if a measurement is performed on one party, the other party, based on the measurement outcomes, will collapse to a corresponding state with some probability and hence gain the average coherence. It is shown that the average coherence is not less than the coherence of its reduced density matrix. In particular, it is very surprising that the extra average coherence (and the maximal extra average coherence with all the possible measurements taken into account) is upper bounded by the classical correlation of the bipartite state instead of the quantum correlation. We also find the sufficient and necessary condition for the null maximal extra average coherence. Some examples demonstrate the relation and, moreover, show that quantum correlation is neither sufficient nor necessary for the nonzero extra average coherence within a given measurement. In addition, the similar conclusions are drawn for both the basis-dependent and the basis-free coherence measure.
相干性是量子力学中最基本的量子特征。对于一个二分量量子态，如果对一方进行测量，另一方基于测量结果将以一定的概率坍缩到相应的状态，从而获得平均相干性。结果表明，平均相干性不小于其约化密度矩阵的相干性。特别地，非常令人惊讶的是，额外的平均相干性（以及考虑所有可能测量的最大额外平均相干性）被二分量态的经典关联而不是量子关联所上界。我们还找到了最大额外平均相干性为零的充分必要条件。一些例子展示了这种关系，而且表明，在给定的测量中，量子关联既不是非零额外平均相干性的充分条件，也不是必要条件。此外，对于基于基和无基的相干性测度，也得到了类似的结论。
