论文标题
单能测量积分波动定理和非标记测量值
Single energy measurement Integral Fluctuation theorem and non-projective measurements
论文作者
论文摘要
我们研究了使用非标记UNSHARP测量的系统中的JARZYSNKI类型平等。观察者从能量测量的结果$ f $中获取的信息，以及随后的条件归一化状态$ \ hatρ（t，f）$演变为最终的最后时间$ t $来定义工作，作为能源的最终期望值与测量结果$ f $之间的差异。获得的jarzynski平等取决于状态在过程中所发展的相干，用于测量能量的仪表的特征以及它引起的噪声。我们详细分析了这些贡献，以揭示其作用。我们表明，在非常特殊的情况下，但通常不是，这种噪声的效果给出了一个因素，即如果使用投影测量值代替非注射性测量值，则将获得的结果。用于监视系统能量的测量值的Unshap特征（定义了仪表的分辨率）导致了不同的感兴趣方案。特别是，如果能量谱中相邻元素之间的距离比仪表的分辨率大得多，则获得了与投影测量案例相似的结果，最多可达到取决于仪表的乘法因子。在相反的情况下，出现了一个更微妙的情况，在该情况下，测量值可能是不明智的，即它们可能不会有助于更新有关系统的信息。在这种情况下，出现对在非重叠案例中获得的关系的纠正。我们分析了这种校正可以忽略的条件。我们还根据进化后的测量状态发展的相干性熵研究了连贯性。我们通过分析由简单仪表监视的两级系统来说明结果。
We study a Jarzysnki type equality for work in systems that are monitored using non-projective unsharp measurements. The information acquired by the observer from the outcome $f$ of an energy measurement, and the subsequent conditioned normalized state $\hat ρ(t,f)$ evolved up to a final time $t$ are used to define work, as the difference between the final expectation value of the energy and the result $f$ of the measurement. The Jarzynski equality obtained depends on the coherences that the state develops during the process, the characteristics of the meter used to measure the energy, and the noise it induces into the system. We analyze those contributions in some detail to unveil their role. We show that in very particular cases, but not in general, the effect of such noise gives a factor multiplying the result that would be obtained if projective measurements were used instead of non-projective ones. The unsharp character of the measurements used to monitor the energy of the system, which defines the resolution of the meter, leads to different scenarios of interest. In particular, if the distance between neighboring elements in the energy spectrum is much larger than the resolution of the meter, then a similar result to the projective measurement case is obtained, up to a multiplicative factor that depends on the meter. A more subtle situation arises in the opposite case in which measurements may be non-informative, i.e. they may not contribute to update the information about the system. In this case, a correction to the relation obtained in the non-overlapping case appears. We analyze the conditions in which such a correction becomes negligible. We also study the coherences, in terms of the relative entropy of coherence developed by the evolved post-measurement state. We illustrate the results by analyzing a two-level system monitored by a simple meter.
