Geometric and Operational Characterization of Two-Qutrit Entanglement

• URL: http://arxiv.org/abs/2601.06783v1
• Date: Sun, 11 Jan 2026 05:44:33 GMT
• Title: Geometric and Operational Characterization of Two-Qutrit Entanglement
• Authors: Ankita Jana,
• Abstract summary: We investigate the entanglement structure of bipartite two-qutrit pure states from both geometric and operational perspectives.<n>We show that the determinant of the coefficient defines a rank-sensitive geometric invariant that vanishes for all rank-2 states.<n>We establish an operational correspondence with three-path optical interferometry and analyze conditional visibility and predictability in a qutrit quantum erasure protocol.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the entanglement structure of bipartite two-qutrit pure states from both geometric and operational perspectives.Using the eigenvalues of the reduced density matrix, we analyze how symmetric polynomials characterize pairwise and genuinely three-level correlations. We show that the determinant of the coefficient matrix defines a natural, rank-sensitive geometric invariant that vanishes for all rank-2 states and is nonzero only for rank-3 entangled states. An explicit analytic constraint relating this determinant-based invariant to the I-concurrence is derived, thereby defining the physically accessible region of two-qutrit states in invariant space. Furthermore, we establish an operational correspondence with three-path optical interferometry and analyze conditional visibility and predictability in a qutrit quantum erasure protocol, including the effects of unequal path transmittances. Numerical demonstrations confirm the analytic results and the associated complementarity relations. These findings provide a unified geometric and operational framework for understanding two-qutrit entanglement.

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