An Exact Five-Step Method for Classicalizing N-level Quantum Systems: Application to Quantum Entanglement Dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915910847037440 |
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| author | Martínez-Gil, Daniel Bargueño, Pedro Miret-Artés, Salvador |
| author_facet | Martínez-Gil, Daniel Bargueño, Pedro Miret-Artés, Salvador |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Exact Five-Step Method for Classicalizing N-level Quantum Systems: Application to Quantum Entanglement Dynamics Martínez-Gil, Daniel Bargueño, Pedro Miret-Artés, Salvador Quantum Physics 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. |
| title | An Exact Five-Step Method for Classicalizing N-level Quantum Systems: Application to Quantum Entanglement Dynamics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.23684 |