Support-Projected Petz Monotone Geometry of Two-Qubit Families: Three-Channel Identity and Non-Reduction of Curvatures

• URL: http://arxiv.org/abs/2509.14578v1
• Date: Thu, 18 Sep 2025 03:27:10 GMT
• Title: Support-Projected Petz Monotone Geometry of Two-Qubit Families: Three-Channel Identity and Non-Reduction of Curvatures
• Authors: Gunhee Cho, Jeongwoo Jae,
• Abstract summary: We investigate the information geometry of pure two-qubit variational families by pulling back arbitrary Petz monotone quantum metrics to circuit-defined submanifolds.<n>This framework strictly generalizes the symmetric logarithmic derivative (SLD/Bures) case and includes, as special examples, the Wigner-Yanase and Bogoliubov-Kubo-Mori metrics.
• Score: 1.227734309612871
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the information geometry of pure two-qubit variational families by pulling back arbitrary Petz monotone quantum metrics to circuit-defined submanifolds and making them intrinsic via support projection onto the active numerical range of the quantum Fisher information tensor. This framework strictly generalizes the symmetric logarithmic derivative (SLD/Bures) case and includes, as special examples, the Wigner-Yanase and Bogoliubov-Kubo-Mori metrics among many others. Our first main theorem proves a universal three-channel decomposition for every Petz monotone metric on any smooth two-parameter slice in terms of the population, coherence, and concurrence of the one-qubit reduction. Second, we show that neither the slice Gaussian curvature nor the ambient scalar curvature of the support-projected metric can, on any nonempty open set, be written as functions solely of concurrence or of the one-qubit entropy. Third, an entanglement-orthogonal gauge isolates the pure entanglement derivative channel and provides intrinsic curvature diagnostics. These results rigorously disprove the expectation that scalar or Gaussian curvatures of finite-dimensional monotone metrics could serve as universal entanglement monotones, extending the counterexamples previously known for the SLD/Bures metric, and complementing recent analyses in Gaussian quantum states. They also furnish a Petz-metric foundation for curvature-aware natural-gradient methods in variational quantum algorithms.

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