Quantum-advantage resource of a two-mode Gaussian state: Analytical theory of convex optimization and a Galois no-go for the closed-form solution

Kunwar Kalra; V. V. Kocharovsky

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arXiv · 2607.00266

Quantum-advantage resource of a two-mode Gaussian state: Analytical theory of convex optimization and a Galois no-go for the closed-form solution

Kunwar Kalra·V. V. Kocharovsky

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Abstract

We study the problem of extracting a quantum complexity resource from a mixed Gaussian state of the multimode light. We present the first complete, certificate-checked solution to this problem in a genuinely coupled sector. We carry this out for the two-mode case, the smallest case in which modes are genuinely coupled. Even in this case the solution is highly nontrivial, and we rigorously prove that it cannot be given in a closed form.

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Kunwar Kalra, V. V. Kocharovsky. 2026-06-30. Quantum-advantage resource of a two-mode Gaussian state: Analytical theory of convex optimization and a Galois no-go for the closed-form solution. https://arxiv.org/abs/2607.00266

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