Comparing quantum complexity and quantum fidelity

• URL: http://arxiv.org/abs/2503.09364v1
• Date: Wed, 12 Mar 2025 13:04:57 GMT
• Title: Comparing quantum complexity and quantum fidelity
• Authors: Nadir Samos Sáenz de Buruaga,
• Abstract summary: We show that complexity provides the same information as quantum fidelity and is therefore capable of detecting quantum phase transitions.<n>We conclude that incorporating a notion of spatial locality into the computation of complexity is essential to uncover new physics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the manifold of Gaussian states, provides the same information as quantum fidelity and is therefore capable of detecting quantum phase transitions. However, it does not offer a more refined analysis than entanglement entropy for a given state. We conclude that incorporating a notion of spatial locality into the computation of complexity is essential to uncover new physics beyond what is accessible through entanglement entropy and fidelity.

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