Randomly spread product states and random Pauli measurements activate all spectral gaps of a Hamiltonian, giving a finite-time quadratic Fisher-information window and enabling simultaneous, beyond-Standard-Quantum-Limit Hamiltonian learning.
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Heisenberg-Limited Quantum Hamiltonian Learning via Randomly Spread Product-States
Randomly spread product states and random Pauli measurements activate all spectral gaps of a Hamiltonian, giving a finite-time quadratic Fisher-information window and enabling simultaneous, beyond-Standard-Quantum-Limit Hamiltonian learning.