We investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross entropy $\chi$ between the bulk measurement outcome distributions in the two circuits acts as an order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and $\chi =1$. In the area law phase $\chi <1$. For circuits with Clifford gates, we provide numerical evidence that $\chi$ can be sampled to accuracy $ϵ$ from $O(1/{ϵ}^2)$ trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the measurement-induced phase transitions is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the “classical” side can be simulated efficiently, while simulating the “quantum” side is still classically hard.

中文翻译：

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测量引起的相变的交叉熵基准

我们研究了使用线性交叉熵来实验访问测量引起的相变而不需要任何量子轨迹后选择的前景。对于两个本体相同但初始状态不同的随机电路，线性交叉熵$\chi$两个电路中的整体测量结果分布之间作为阶参数，可用于区分体积定律和面积定律阶段。在体积定律阶段（和热力学极限），体积测量无法区分两种不同的初始状态，并且$\chi =\mathrm{1个}$. 在区域法阶段$\chi <\mathrm{1个}$. 对于带有克利福德门的电路，我们提供了数字证据$\chi$可以精确采样$\epsilon$从$欧(\mathrm{1个}/{\epsilon }^{\mathrm{2个}})$轨迹，通过在没有后选择的情况下在量子模拟器上运行第一个电路，在第二个经典模拟的帮助下。我们还发现，对于弱去极化噪声，测量引起的相变特征仍然存在于中等大小的系统中。在我们的协议中，我们可以自由选择初始状态，以便可以有效地模拟“经典”方面，而模拟“量子”方面仍然很难经典。