论文标题
部分可观测时空混沌系统的无模型预测
Essential role of quantum speed limit in violation of Leggett-Garg inequality across a PT-transition
论文作者
论文摘要
我们研究了由非线性BLOCH方程（衍生在J.Phys。A：Math。Aphile。54，115301（2021））的两级系统（TLS）的Leggett-Garg不平等（LGI）（TLS）。我们提出了最大违反LGI的参数空间的代数标识（尤其是$ k_ {3} $）。在PT-对称制度中，始终发现$ k_ {3} $的最大值大于$ 3/2 $的量子绑定（lüdersbound），但总体上未达到$ k_ {3} = 3 $的代数最大值。 However, in the limit where PT-symmetry breaking parameter approaches the exceptional point from the PT-symmetric side, $K_{3}$ is found to asymptotically approach its algebraic maximum of 3. In contrast, the maximum value of $K_{3}$ always reaches its algebraic maximum in the PT-broken phase $i.e.$ $K_{3}\rightarrow 3$.我们发现（i）进化速度（SOE）必须达到其最大值（在初始状态的参数空间以及连续测量之间的时间间隔），以促进$ k_ {3} \ rightArrow 3 $，（ii）的价值，即在状态进化过程中其最小值等于零。实际上，我们表明，最小进化速度可以用作订单参数，该参数在PT对称侧是有限的，在PT折叠侧相同。最后，我们通过量子测量讨论了该动力学的可能实验实现，然后在三级原子与腔模式的三个级别的选择后进行了选择后，经历了Lindbladian动力学。
We study Leggett-Garg inequality (LGI) of a two level system (TLS) undergoing non-Hermitian dynamics governed by a non-linear Bloch equation (derived in J. Phys. A: Math. Theor. 54, 115301 (2021)) across a PT-transition. We present an algebraic identification of the parameter space for the maximum violation of LGI (in particular $K_{3}$). In the PT-symmetric regime the maximum allowed value for $K_{3}$ is always found to be greater than the quantum bound (Lüders bound) of $3/2$ but it does not reach the algebraic maximum of $K_{3}=3$ in general. However, in the limit where PT-symmetry breaking parameter approaches the exceptional point from the PT-symmetric side, $K_{3}$ is found to asymptotically approach its algebraic maximum of 3. In contrast, the maximum value of $K_{3}$ always reaches its algebraic maximum in the PT-broken phase $i.e.$ $K_{3}\rightarrow 3$. We find that (i) the speed of evolution (SOE) must reach its maximum value (in the parameter space of initial state and the time interval between successive measurements) to facilitate the value of $K_{3} \rightarrow 3$, (ii) together with the constraint that its minimum value must run into SOE equals to zero during the evolution of the state. In fact we show that the minimum speed of evolution can serve as an order parameter which is finite on the PT-symmetric side and identically zero on the PT-broken side. Finally, we discuss a possible experimental realization of this dynamics by quantum measurement followed by post-selection procedure in a three level atom coupled to cavity mode undergoing a Lindbladian dynamics.
