2025/04/21 by Maximilian Goll, Robert H. Jonsson, Goll, Maximilian +1 · 3 voices
Computer Science · Physics and Astronomy · #Bounding overwatch #Conjecture #Connection (principal bundle) #Harmonic oscillator #Limit (mathematics) #Metric (unit) #Quantum Information and Cryptography #Quantum chaos and dynamical systems #Quantum many-body systems #Space (punctuation) #State (computer science) #State space
paper · pdf · doi:10.22331/q-2026-07-15-2160
openalex publication_date 2026/07/15 · rss pubdate 2026/07/15 · openalex created_date 2026/07/16 · openalex updated_date 2026/08/05
Quantum 10, 2160 (2026). https://doi.org/10.22331/q-2026-07-15-2160 The preparation of quantum many-body systems faces the difficulty that in a realistic scenario only few control parameters of the system may be accessible. In this context, an interesting connection between the energy fluctuations during state preparation and its geometric length as measured by the Fubini-Study metric was discussed by Bukov et al. in 2019 [ 5 ]. An inspiring conjecture lower bounding the energy fluctuations by the minimal geometric length of all accessible state preparation protocols was put forward together with supporting examples and numerical evidence. However, we here show that the conjecture does not hold but can be violated if the accessible parameter space has extrinsic curvature, when embedded into the space of all dynamically accessible states. We illustrate this by a number of generic qubit, qutrit and harmonic oscillator systems.