The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cramér-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less attention has been paid to non-Hermitian systems. In this talk, working with different logarithmic operators, we derive two previously unknown expressions for quantum Fisher information, and two Cramér-Rao bounds lower than the well-known one are found for non-Hermitian systems. These lower bounds are due to the merit of non-Hermitian observable and it can be understood as a result of extended regimes of optimization. Two experimentally feasible examples are presented to illustrate the theory, saturation of these bounds and estimation precisions beyond the Heisenberg limit are predicted and discussed. A setup to measure non-Hermitian observable is also proposed.

衣学喜，男，1968年4月生, 博士，东北师范大学特聘教授，博士生导师。本科和硕士毕业于东北师范大学，博士毕业于吉林大学。先后在中国科学院理论物理研究所、德国Essen大学、德国汉诺威大学、美国佐治亚理工学院、新加坡国立大学、香港大学和澳大利亚新南威尔士大学从事过博士后(访问学者)研究工作。2003-2013就职于大连理工大学，从2013年至今任现职。他对量子开放系统及其应用，如量子控制、量子器件、量子度量学感兴趣。在Phys. Rev.系列发表文章130余篇, 合著4部教材和学术专著。2016获吉林省科学技术(自然科学类)一等奖。