Quantum chaos and macroscopic realism as no-signaling in time

TL;DR

The paper investigates how chaos influences macrorealism tests by studying NSIT violations in a quantum chaotic system, the kicked top. By linking the NSIT conditional probability to a 3-OTOC and introducing coherence-based disturbances, the authors show that chaotic dynamics amplify NSIT violations, with the effect depending on initial state and the time between measurements. Using two measures (Hellinger distance and a participation-ratio-based metric) and two coherent initial states, they demonstrate that chaos induces strong, sometimes saturating NSIT disturbances as $\kappa_0$ grows, and that these effects scale with system size $j$. The findings establish a qualitative semiclassical picture that connects macroscopic realism tests to quantum chaos via a 3-OTOC, and they highlight coherence as a key resource in macrorealism violations, with potential implications for macroscopic quantum coherence experiments.

Abstract

Macroscopic realism is a set of assumptions about how we experience the world at a classical level. While the Leggett-Garg inequalities are temporal correlations that are violated by quantum systems not obeying such macrorealism, the no-signaling in time condition is also a necessary condition. This compares measurement outcomes with and without prior measurements. As dynamics and correlations play a central role in these measures, this paper explores the effects of regular versus chaotic dynamics on the violations of macroscopic realism. We observe a close connection between a 3 point out-of-time-order correlator and the conditional probabilities of measurement, and we find unmistakable imprints of chaos on the violations of macrorealism. We provide qualitative semiclassical reasoning for the numerical results involving a kicked top, and for two important initial states that behave very differently.

Figures (10)

• Figure 1: The measurement timeline. Time increases along the axis towards right.
• Figure 2: The distances $\Delta_1$ and $H_1$, for $n=1$ in the absence of chaos: $\kappa_0=0$, as a function of Alice's measurement time $t_\alpha$. The constant line is for the initial state $|\vb{\hat{y}}, j\rangle$, while the oscillatory curvem vanishing for even $t_{\alpha}$ is for the initial state $|\vb{\hat{z}},j\rangle$. Due to continuity, this effect persists for small non-zero values of $\kappa_0$ as well.
• Figure 3: The distances $\Delta_n$ and $H_n$, averaged over $T=50$ initial times $t_\alpha$. For the initial state $\op{\vb{\hat{z}}, j}, j=15$, Alice measures $J_z$ at $t_{\alpha}$ while Bob measures $J_z$ at $t_{\alpha}+n$.
• Figure 4: Same as the previous figure, except that the initial state is $\rho_0= \op{\vb{\hat{y}}, j}$. Several features are as they were in the case of $| \mathbf{\hat{z}},j\rangle$. Note however, that the peaks occur around $\kappa_0=2$ where the fixed point loses its stability. For small $\kappa_0$, the prominent difference for different $n$ values arises because of time evolution for the state localized in the regular region.
• Figure 5: The distance measures are shown including odd and even intervals in the range $1 \leq n \leq 5$. for the initial state$|\mathbf{\hat{z}},j\rangle$ (left) the odd/even effect persists well into the fully chaotic regime. For the $|\mathbf{\hat{y}},j\rangle$ case (right), for low $\kappa_0$ values, the proximity to rotation about the $y-$axis produces the difference which vanishes with the onset of chaos.