一种与开放系统初态无关的非马尔科夫度量

Non-Markovian measure independent of initial states of open systems

近年来,量化开放量子系统中的非马尔科夫效应已经成为了量子消相干控制领域研究中的一个重要科学问题.本文对于单个开放的两能级系统,将基于量子Fisher信息的非马尔科夫度量从系统初态为纯态的情况推广到系统初态为任意态的情况.作为该非马尔科夫度量的应用,分别研究了利用量子Fisher信息在检测一个两能级系统受到零温度振幅耗散通道、相位衰减通道和随机幺正通道作用时对应非马尔可夫过程发生满足的条件.研究结果显示:一个相位参数的量子Fisher信息对这三种衰减通道的非马尔科夫过程发生所满足的条件与系统初态的选择是无关的.进一步,对于振幅耗散通道和相位衰减通道,非马尔科夫过程发生的条件同基于迹距离、映射的可分性、量子互信息和量子Fisher信息矩阵等给出的条件是等价的.如预期的一样,对于振幅耗散通道情况且选择系统初态为最优化纯态时,相应的结果正是Lu等获得的结果(Lu X M,Wang X G,Sun C P 2010 Phys.Rev.A 82042103);而对于随机幺正通道,其马尔可夫过程发生的条件同基于迹距离、映射的可分性、量子互信息和量子Fisher信息矩阵等给出的条件是不完全等价的.另外,得到了一个有趣的关系:在这三种耗散通道模型中系统演化态的量子l范数相干性的平方正好等于相位参数的量子Fisher信息.总之,本文得到的结果不仅完善了用量子Fisher信息来检测开放系统中非马尔科夫效应的应用范围,同时也进一步彰显了量子Fisher信息在量子信息处理中独特的作用.

In recent years,quantifying non-Markovian effect in open quantum system has become an important subject in the quantum decoherence control field.In this paper,a non-Markovian measure independent of the initial state of open system is proposed,thereby extending non-Markovian measure based on quantum Fisher information from the case where the initial state of the system is a pure state to the case where the initial state of the system is an arbitrary mixed state.As its application,the non-Markovian process is quantified by quantum Fisher information about a two-level system undergoing the three well-known dissipative channels,i.e.amplitude dissipative channel,phase damping channel,and random unitary channel.The results show that the conditions of non-Markovian processes in the three dissipative channels are independent of the selection of the initial state of the system by means of the quantum Fisher information of a phase parameter.Further,for amplitude dissipation channel and phase damping channel,the conditions for the non-Markovian processes to occur are equivalent to those given by trace distance,divisibility,quantum mutual information,quantum Fisher-information matrix,et al.As expected,for the case of amplitude dissipation channel,the corresponding results can reduce to the one in other paper(Lu X M,Wang X G,Sun C P 2010 Phys.Rev.A 82042103)by selecting the initial state of the system as an optimal pure state.However,for random unitary channel,the conditions of non-Markovian process are not equivalent to those for other measures.In addition,we also obtain an interesting relationship between quantum Fisher information and quantum coherence of the open system in the three dissipative channels,namely the square of quantum lcoherence for the evolved state of system is exactly equal to the quantum Fisher information of the phase parameter.In a word,the obtained results not only improve the application scope of using the quantum Fisher information to detect non-Markovian effects in open systems,but also further highlight its important role in quantum information processing.