Derives QFI duality F_Q(w^T θ) + F_Q(v^T θ) ≤ N for orthogonal unit vectors w, v in N-qubit states, with equality cases for equatorial and GHZ states, implying privacy when precision saturates the Heisenberg limit.
Theorem 1.For any two unit vectors ˆw⊥ ˆv: FQ( ˆw⊤θ) +F Q(ˆv⊤θ)≤N.(7) Equality holds with equatorial probe states forN= 2
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Precision and Privacy in Distributed Quantum Sensing: A Quantum Fisher Information Duality
Derives QFI duality F_Q(w^T θ) + F_Q(v^T θ) ≤ N for orthogonal unit vectors w, v in N-qubit states, with equality cases for equatorial and GHZ states, implying privacy when precision saturates the Heisenberg limit.