Comparing quantum complexity and quantum fidelity
arXiv:2503.09364 · doi:10.1103/PhysRevB.111.245107
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.
arXiv commentmain:7pages. appendices: 8 pages + 4. 8 figures. This is a pre-publication version, with minor differences from the final published article
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