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

• URL: http://arxiv.org/abs/2506.23684v1
• Date: Mon, 30 Jun 2025 10:06:37 GMT
• Title: An Exact Five-Step Method for Classicalizing N-level Quantum Systems: Application to Quantum Entanglement Dynamics
• Authors: Daniel Martínez-Gil, Pedro Bargueño, Salvador Miret-Artés,
• Abstract summary: We present a general and exact method for classicalizing the dynamics of any $N$-level quantum system.<n>The method can be expressed as five-step algorithmic procedure to derive a classical Hamiltonian and a symplectic structure for the Poisson brackets.<n>We demonstrate the method's efficacy by classicalizing two interacting qubits in $mathbbCP3$, exactly reproducing quantum observables such as quantum probabilities, quaternionic population differences and the concurrence.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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