论文标题
两个随机状态的子系统痕量距离
Subsystem Trace-Distances of Two Random States
论文作者
论文摘要
我们研究混沌量子系统中的两州歧视。假设已随机选择了两个$ n $ qubit的纯状态之一，则可以从涉及$ n-n_b $ Qubits子集的最佳选择实验中正确识别所选状态的概率，由$ n_b $ qubits的痕量距离给出，并部分差一点。在热力学限制$ n \至\ infty $中，随机纯状态的平均子系统痕量距离使从统一到零f = 1/2 $的急剧，一阶的过渡，因为分数$ f = n_b/n $未衡量的量子的n_b/n $增加了。我们通过分析计算有限数量$ n $ Qubits的相应跨界，研究它如何受到局部保护法的影响，并测试我们针对多体混乱模型的确切对角线化的预测。
We study two-state discrimination in chaotic quantum systems. Assuming that one of two $N$-qubit pure states has been randomly selected, the probability to correctly identify the selected state from an optimally chosen experiment involving a subset of $N-N_B$ qubits is given by the trace-distance of the states, with $N_B$ qubits partially traced out. In the thermodynamic limit $N\to\infty$, the average subsystem trace-distance for random pure states makes a sharp, first order transition from unity to zero at $f=1/2$, as the fraction $f=N_B/N$ of unmeasured qubits is increased. We analytically calculate the corresponding crossover for finite numbers $N$ of qubits, study how it is affected by the presence of local conservation laws, and test our predictions against exact diagonalization of models for many-body chaos.
