An exact five-step method for classicalizing N-level quantum systems: Application to quantum entanglement dynamics

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 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 CP 3 , exactly reproducing quantum observables such as quantum probabilities, population differences, and the concurrence, capturing entanglement dynamics via a classical analog.