Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators
arXiv:2503.00918 · doi:10.1103/s1t6-6brz
Abstract
Quantum operator scrambling describes the spreading of local operators into the whole system in the picture of Heisenberg evolution, which is often quantified by the operator size growth. Here we propose a measure of quantum operator scrambling via Holevo information of operators, by taking its capacity to distinguish operator information locally. We show that the operator size is closely related to a special kind of Holevo information of operators. Moreover, we propose a feasible protocol for measuring Holevo information of operators on digital quantum simulators based on random states. \textcolor{black}{For the mixed-field Ising model,} our numerical simulations show that the integrable system can be told apart from the chaotic system by measuring the spatial-temporal patterns of Holevo information. Furthermore, we find that error mitigation is required to restore the time-oscillation behavior of Holevo information for the integrable system, a crucial feature distinct from the chaotic one. Our work provides a new perspective to understand the information scrambling and quantum chaos from aspects of Holevo information of operators.
8 pages, 6 figures
References in corpus (44)
- Black holes as mirrors: quantum information in random subsystems
- Error mitigation for short-depth quantum circuits
- Characterizing Quantum Supremacy in Near-Term Devices
- Operator Spreading in Random Unitary Circuits
- Validating quantum computers using randomized model circuits
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Measuring the scrambling of quantum information
- Theory of universal incoherent metallic transport
- Chaos and complexity by design
- A Universal Operator Growth Hypothesis
- Information Scrambling in Computationally Complex Quantum Circuits
- Coding Theorems for Quantum Channels
- Solvable model for a dynamical quantum phase transition from fast to slow scrambling
- Does scrambling equal chaos?
- Scrambling and entanglement spreading in long-range spin chains
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Krylov complexity from integrability to chaos
- Approximate unitary -designs by short random quantum circuits using nearest-neighbor and long-range gates
- Quantum butterfly effect in weakly interacting diffusive metals
- Black holes, quantum information, and unitary evolution
- Chaos and Complexity in Quantum Mechanics
- Disentangling Scrambling and Decoherence via Quantum Teleportation
- Quantum Dynamics as an analog of Conditional Probability
- Strange metal from local quantum chaos
- Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
- Spectral Lyapunov exponents in chaotic and localized many-body quantum systems
- Probing Operator Spreading via Floquet Engineering in a Superconducting Circuit
- Quantum Information Scrambling in Quantum Many-body Scarred Systems
- Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
- Super-exponential scrambling of Out-of-time-ordered correlators
- Super-exponential diffusion in nonlinear non-Hermitian systems
- Scaling laws of the out-of-time-order correlators at the transition to the spontaneous -symmetry breaking in a Floquet system
- Distinguishing Black Hole Microstates using Holevo Information
- Information-Theoretic Memory Scaling in the Many-Body Localization Transition
- Operator Size Distribution in Large Quantum Mechanics of Majorana Fermions
- Extracting randomness from magic quantum states
- Lieb-Robinson Bound at Finite Temperature
- Quantum algorithm for evaluating operator size with Bell measurements
- Approximating quantum channels by completely positive maps with small Kraus rank
- Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
- Surface criticality in the mixed-field Ising model with sign-inverted next-nearest-neighbor interaction
- Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
- Chaos and the dynamics of information in dissipative electronic systems