Deciding the Attainability of the Multiparameter Quantum Fisher Information is NP-Hard

arXiv:2609.35975 · quant-ph · Submitted 2026-09-28 · Read on arXiv

quant-ph

Submitted: 2026-09-28

Updated: 2026-09-28

Comments: 5 pages, comments very welcome

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Hilbert Space — 8× in this paper · explained in 2 episodes
• Fisher Information — 7× in this paper · explained in 3 episodes
• Entanglement — 6× in this paper · explained in 3 episodes
• Trace — 6× in this paper · explained in 2 episodes
• Verifier — 4× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Kernel decomposition — 2× in this paper · explained in 2 episodes
• Multipartite Entanglement — 2× in this paper · explained in 2 episodes
• Quantum Fisher Information (QFI) — 2× in this paper · explained in 13 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes

Sources

• $100\pm\Delta t$ Years of Quantum Uncertainty: From Origins to Modern Insights
• Saturating the Quantum Cram'er--Rao Bound in Prioritised Parameter Estimation
• Beating three-parameter precision trade-offs with entangling collective measurements
• Quantum state estimation with nuisance parameters
• Sufficient support size of measurements for quantum estimation
• Hierarchy of saturation conditions for multiparameter quantum metrology bounds
• QestOptPOVM: An iterative algorithm to find optimal measurements for quantum parameter estimation
• The gap persistence theorem for quantum multiparameter estimation

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