The growth of operator entropy in operator growth

Abstract

We study upper bounds on the growth of operator entropy $S_K$ in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth rate $|{\partial }_t{S}_K|\le 2b_1\Delta S_K$, where $b_1$ is the first Lanczos coefficient and $\Delta S_K$ is the variance of $S_K$. However, for irreversible process, this bound generally turns out to be too loose at long times. We further find a tighter bound in the long time limit using a universal logarithmic relation between Krylov complexity and operator entropy. The new bound describes the long time behavior of operator entropy very well for physically interesting cases, such as chaotic systems and integrable models.

arXiv commentminor corrections,19 pages, 4 figures

References in corpus (12)

• A bound on chaos
• A Universal Operator Growth Hypothesis
• Quantum chaos and the complexity of spread of states
• Operator complexity: a journey to the edge of Krylov space
• On The Evolution Of Operator Complexity Beyond Scrambling
• Krylov complexity in conformal field theory
• Complexity growth of operators in the SYK model and in JT gravity
• Ultimate Speed Limits to the Growth of Operator Complexity
• Operator Delocalization in Quantum Networks
• Krylov Complexity in Quantum Field Theory
• Universal relation for operator complexity
• Probing the entanglement of operator growth

Cited by in corpus (7)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov Complexity in Open Quantum Systems
• Krylov complexity in large-$q$ and double-scaled SYK model
• A universal approach to Krylov State and Operator complexities
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Universal Hypothesis of Autocorrelation Function from Krylov Complexity
• Krylov Complexity of Fermionic and Bosonic Gaussian States