Effects of symmetries on quantum fidelity decay

2005/02/01 by Yaakov S. Weinstein, C. Stephen Hellberg · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Chaotic #Computer science #Counterintuitive #Exponential decay #Exponential function #Fidelity #Homogeneous space #Mathematical analysis #Mathematics #Perturbation (astronomy) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Statistical physics #quant-ph

paper · pdf · doi:10.1103/physreve.71.035203

published as Phys. Rev. E 71, 035203(R), 2005 · 5 pages, 3 figures, to be published Phys. Rev. E Rapid Communication

arxiv created 2005/02/01 · openalex publication_date 2005/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We explore the effect of a system's symmetries on fidelity decay behavior. Chaoslike exponential fidelity decay behavior occurs in nonchaotic systems when the system possesses symmetries and the applied perturbation is not tied to a classical parameter. Similar systems without symmetries exhibit faster-than-exponential decay under the same type of perturbation. This counterintuitive result, that extra symmetries cause the system to behave in a chaotic fashion, may have important ramifications for quantum-error correction.

Citations

• Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states
• Decay of the Loschmidt Echo for Quantum States with Sub-Planck-Scale Structures
• Decay of the classical Loschmidt echo in integrable systems
• Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
• Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Classical versus quantum errors in quantum computation of dynamical systems
• Characteristic Vectors of Bordered Matrices With Infinite Dimensions

Cited by

• Dynamics of Loschmidt echoes and fidelity decay