量子首次检测问题的运行测量协议
Running Measurement Protocol for the Quantum First-detection problem
摘要：
量子步行者的检测统计问题受到越来越多的关注，因为它与量子搜索问题有关。我们研究了采用移动检测器的效果，使用固定采样时间$τ$的投影测量方法，检测器在每次检测尝试之前移动。对于线上的紧束缚量子行走，移动的检测器允许人们瞄准行走者的特定群速度范围，定性地修改量子首次检测概率的行为。我们映射的问题，一个固定的检测器与修改后的酉演化算子，并使用已建立的方法来解决这个问题，研究第一检测统计的移动检测器上的有限环和无限的一维晶格。在线上，系统在临界值$τ$处表现出动态相变，从检测时间呈指数下降且总检测非常小的状态到具有幂律衰减且检测到粒子的概率显著更高的状态。描述在该临界$τ$处的检测概率的幂律衰减的指数是10/3，而对于每个较大的$τ$是3。此外，移动的探测器强烈地修改了芝诺效应。
英文摘要：
The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement approach with fixed sampling time $τ$, with the detector moving right before every detection attempt. For a tight-binding quantum walk on the line, the moving detector allows one to target a specific range of group velocities of the walker, qualitatively modifying the behavior of the quantum first-detection probabilities. We map the problem to that of a stationary detector with a modified unitary evolution operator and use established methods for the solution of that problem to study the first-detection statistics for a moving detector on a finite ring and on an infinite 1D lattice. On the line, the system exhibits a dynamical phase transition at a critical value of $τ$, from a state where detection decreases exponentially in time and the total detection is very small, to a state with power-law decay and a significantly higher probability to detect the particle. The exponent describing the power-law decay of the detection probability at this critical $τ$ is 10/3, as opposed to 3 for every larger $τ$. In addition, the moving detector strongly modifies the Zeno effect.
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