Department of Physics, Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.
Quantinuum, Leopoldstrasse 180, 80804 Munich, Germany.
Phys Rev Lett. 2023 Jun 9;130(23):230401. doi: 10.1103/PhysRevLett.130.230401.
We consider Gaussian quantum circuits that alternate unitary gates and postselected weak measurements, with spatial translation symmetry and time p eriodicity. We show analytically that such models can host different kinds of measurement-induced phase transitions detected by entanglement entropy, by mapping the unitary gates and weak measurements onto Möbius transformations. We demonstrate the existence of a log-law to area-law transition, as well as a volume-law to area-law transition at a finite measurement amplitude. For the latter, we compute the critical exponent ν for the Hartley, von Neumann and Rényi entropies exactly.
我们考虑具有空间平移对称性和时间周期性的幺正门和后选弱测量交替的高斯量子电路。我们通过将幺正门和弱测量映射到 Möbius 变换，分析表明这种模型可以容纳不同种类的通过纠缠熵检测到的测量诱导相变。我们展示了对数律到面积律的转变，以及在有限测量幅度下的体积律到面积律的转变。对于后者，我们精确计算了 Hartley、von Neumann 和 Rényi 熵的临界指数 ν。
