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arXiv · 2506.23684

An Exact Five-Step Method for Classicalizing N-level Quantum Systems: Application to Quantum Entanglement Dynamics

Daniel Martínez-Gil·Pedro Bargueño·Salvador Miret-Artés
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Abstract

In this manuscript, we present a general and exact method for classicalizing the dynamics of any $N$-level quantum system, transforming quantum evolution into a classical-like framework using the geometry of complex projective spaces $\mathbb{CP}^{N-1}$. The method can be expressed as five-step algorithmic procedure to derive a classical Hamiltonian and a symplectic structure for the Poisson brackets, yielding $N-1$ Hamilton's equations that precisely replicate the quantum dynamics, including complex phenomena like entanglement. We demonstrate the method's efficacy by classicalizing two interacting qubits in $\mathbb{CP}^3$, exactly reproducing quantum observables such as quantum probabilities, quaternionic population differences and the concurrence, capturing entanglement dynamics via a classical analog.

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Daniel Martínez-Gil, Pedro Bargueño, Salvador Miret-Artés. 2025-06-30. An Exact Five-Step Method for Classicalizing N-level Quantum Systems: Application to Quantum Entanglement Dynamics. https://doi.org/10.1016/j.aop.2026.170425

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