Entanglement and Quantum Coherence in Krylov Space Dynamics

• URL: http://arxiv.org/abs/2603.26619v1
• Date: Fri, 27 Mar 2026 17:15:24 GMT
• Title: Entanglement and Quantum Coherence in Krylov Space Dynamics
• Abstract summary: We study the spreading of quantum states in Krylov space under unitary dynamics.<n> Quantifiers of this spreading, such as the spread complexity and the inverse participation ratio, depend explicitly on both the Hamiltonian and the initial state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The spreading of quantum states in Krylov space under unitary dynamics provides a natural framework for characterizing quantum complexity. Quantifiers of this spreading, such as the spread complexity and the inverse participation ratio, depend explicitly on both the Hamiltonian and the initial state, rendering their connection to fundamental quantum resources such as entanglement and quantum coherence subtle. We establish quantitative bounds relating Krylov-space spreading to the entanglement of the evolved state and to the quantum coherence of the initial state. For bipartite systems, we have shown that the entanglement of the evolved state is upper bounded in terms of the entanglement of the Krylov basis vectors and the spread complexity. In the case of multipartite systems, analogous bounds are obtained for the inverse participation ratio, a quantifier of the delocalization of a quantum state in the Krylov basis, in terms of the geometric measures. Furthermore, for qubit and qutrit systems, we derive relations between the quantum coherence of the initial state in the energy eigenbasis and the spread complexity, valid for arbitrary Hamiltonians. Our results provide quantitative constraints linking Krylov-space complexity growth to fundamental quantum resources.

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