Entanglement and non-local magic in a non-unitarily deformed non-Hermitian bipartite system

• URL: http://arxiv.org/abs/2608.08346v1
• Date: Sat, 08 Aug 2026 21:59:53 GMT
• Title: Entanglement and non-local magic in a non-unitarily deformed non-Hermitian bipartite system
• Abstract summary: A Hermitian operator with a degenerate eigenspace is transformed by an invertible non-unitary similarity map.<n> Entanglement grows monotonically with the non-Hermiticity parameter.<n>In larger bipartite spaces, the Page entropy and Haar-averaged purity provide reference values for eigenstate typicality.
• Score: 1.0293849768864847
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Hermitian degeneracies are usually discussed through spectral coalescence, whereas entanglement is a property of eigenvectors and need not be fixed by the eigenvalues alone. We formulate a compact bipartite model that separates these two notions. A Hermitian operator with a degenerate eigenspace is transformed by an invertible non-unitary similarity map. The resulting Hamiltonian is non-Hermitian and retains a non-defective degeneracy at every finite value of the non-Hermiticity parameter. For an exactly solvable two-qubit realization, the right eigenstates evolve continuously from product states to maximally entangled states although the spectrum is unchanged. We distinguish the positive right-state reduced density matrix from the generally non-positive biorthogonal reduction, for which entropy may become complex. The same two-qubit solution gives a closed partial-transpose negativity and a Schmidt-gauged non-local magic. Entanglement grows monotonically with the non-Hermiticity parameter, whereas the non-local magic vanishes for both the product and maximally entangled limits and is largest at an intermediate coupling. In larger bipartite spaces, the Page entropy and Haar-averaged purity provide reference values for eigenstate typicality. These diagnostics separate non-defective degeneracy, exceptional-point sensitivity, Haar-typical entanglement, and non-stabilizer correlations without relying on a proliferation of basis-dependent spectral quantities.

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