Harish-Chandra Research Institute: Haar-Averaged Sum of Total Correlations Probes System Integrability

Researchers at the Harish-Chandra Research Institute have introduced a method for measuring quantum information scrambling. The team introduces the “Haar-averaged sum of total correlations,” or aSTC, and demonstrates its ability to differentiate between integrable and chaotic dynamics using long-range quantum X Y Z XYZ spin models. Unlike established methods, the aSTC, coupled with average genuine multipartite entanglement, distinguishes between system behaviors even when out-of-time-ordered correlators (OTOCs) fail in non-Markovian systems. This work demonstrates that the long-time average and, importantly, the temporal fluctuations of the aSTC provide a faithful and system-size-independent signature of integrable and chaotic dynamics, similar to the conventional measure of scrambling, OTOC.

A new approach to charting the chaotic behavior of quantum systems reveals a surprising resilience in measuring information scrambling, even when standard methods falter. Researchers at the Harish-Chandra Research Institute are introducing the “Haar-averaged sum of total correlations (aSTC)” as a robust alternative to the out-of-time-ordered correlator (OTOC) for analyzing how quantum information spreads. The team demonstrated this distinction using a model where the integrable limit is the nearest-neighbor transverse X Y XY model, revealing that both the average and, crucially, the temporal fluctuations of the aSTC provide a faithful and system-size-independent signature of integrable and chaotic dynamics, similar to the OTOC. In non-Markovian systems, where information backflow restores the scrambling dynamics, the aSTC retains its distinguishing power even at intermediate times. When the system is in contact with the thermal reservoir and system-bath coupling follows Markovianity, the fluctuations of the aSTC and OTOC continue to distinguish integrable and chaotic dynamics only at intermediate times.

Distinguishing between integrable and chaotic quantum systems has long relied on operator-based measures like out-of-time-ordered correlators (OTOCs), but a new approach utilizing state-based diagnostics is gaining traction. This work expands beyond closed quantum systems to address the impact of environmental interaction. While Markovian noise, where system-bath coupling is memoryless, typically erases the ability of both OTOCs and aSTC to differentiate between system types at intermediate times, the researchers found these fluctuations still offer a distinguishing capability. More surprisingly, in non-Markovian scenarios, information backflow restores the scrambling dynamics, enabling the aSTC to retain its distinguishing power even when OTOCs fail. “Interestingly, we exhibit that, under Markovian amplitude damping and non-Markovian dephasing noise, the temporal fluctuations of the aSTC can discriminate between integrability and non-integrability in the weak Markovian regime, even when OTOC fails to do so.”

The aSTC’s performance extends beyond closed quantum systems, addressing the impact of environmental interactions. In the non-Markovian domain, information backflow restores the scrambling dynamics, enabling the aSTC to retain its distinguishing power even at long times.

The ability to discern order from chaos at the quantum level has implications for designing more robust quantum technologies and understanding fundamental physics, and new research highlights a refined method for doing so. This model’s integrable limit is specifically the nearest-neighbor transverse XY model, providing a well-defined benchmark for comparison. The team found that not only the long-time average but, crucially, the temporal fluctuations of the aSTC provide a faithful and system-size-independent signature of integrable and chaotic dynamics, similar to the conventional measure of scrambling, out-of-time-ordered correlator (OTOC) method.

Conventional methods for detecting quantum chaos, like out-of-time-ordered correlators (OTOCs), rely on tracking operator evolution, a process demanding precise control over quantum systems. The team’s investigations reveal a surprising resilience in the aSTC’s performance, particularly when systems aren’t behaving as expected. Unlike established methods, the aSTC, coupled with average genuine multipartite entanglement, distinguishes between system behaviors even when OTOCs fail. When the system is in contact with the thermal reservoir and system-bath coupling follows Markovianity, the fluctuations of the aSTC and OTOC continue to distinguish integrable and chaotic dynamics only at intermediate times. However, in the non-Markovian domain, information backflow restores the scrambling dynamics, enabling the aSTC to retain its distinguishing power.

The ability of quantum systems to maintain distinctions between order and chaos diminishes as they interact with their environment, but a newly examined metric demonstrates surprising resilience. In the non-Markovian domain, information backflow restores the scrambling dynamics, enabling the aSTC to retain its distinguishing power even at long times. Interestingly, under Markovian amplitude damping and non-Markovian dephasing noise, the temporal fluctuations of the aSTC can discriminate between integrability and non-integrability in the weak Markovian regime, even when OTOC fails to do so.

Non-Markovian Effects Restoring Scrambling Dynamics

The pursuit of reliable metrics for quantum chaos has traditionally centered on operator-based approaches like the out-of-time-ordered correlator (OTOC), but recent work demonstrates the potential of state-based measurements to offer complementary insights into system dynamics. Researchers at the Harish-Chandra Research Institute are investigating whether these alternative methods can maintain their diagnostic power when quantum systems are subject to environmental noise, a crucial consideration for real-world applications. However, the study highlights a surprising resilience in the aSTC when moving beyond Markovianity. Unlike established methods, the aSTC, coupled with average genuine multipartite entanglement, continues to distinguish between system behaviors even when OTOCs fail. This is significant because, in the non-Markovian domain, information backflow restores the scrambling dynamics, enabling the aSTC to retain its distinguishing power even at long times.

The team found that not only the long-time average but, crucially, the temporal fluctuations of the aSTC provide a faithful and system-size-independent signature of integrable and chaotic dynamics, similar to the conventional measure of scrambling, out-of-time-ordered correlator (OTOC). When the system is in contact with the thermal reservoir and system-bath coupling follows Markovianity, the fluctuations of the aSTC and OTOC continue to distinguish integrable and chaotic dynamics only at intermediate times.

Their work demonstrates the aSTC’s resilience in the face of environmental noise, a critical factor often overlooked in theoretical models. While conventional measures like the out-of-time-ordered correlator (OTOC) struggle to maintain this distinction when systems interact with their environment following Markovian rules, the aSTC retains its distinguishing power even at intermediate times.

Researchers focused on multipartite entanglement, correlations between multiple quantum particles, generated from initially uncorrelated states, measuring quantum scrambling, the process by which localized information disperses. This approach moves beyond simply observing the dynamics of a system to actively measuring the creation of quantum connections. Notably, the study extends to systems interacting with their environment, a common challenge in real-world applications.