Precision measurements at the interface between unitary and non-unitary encoding

• URL: http://arxiv.org/abs/2606.10529v1
• Date: Tue, 09 Jun 2026 08:00:43 GMT
• Title: Precision measurements at the interface between unitary and non-unitary encoding
• Abstract summary: We derive analytic precision expressions for both the unitary parameter $$ and the dissipation strength $$.<n>For unitary encoding, the optimal encoding time is independent of $N$, yielding the Heisenberg limit $propto 1 / N$.<n>For non-unitary encoding, the precision is insensitive to intrinsic dynamics and encoding time, scaling as $propto sqrt/ expval*hatLdagger hatL$.
• Score: 5.6357907888795085
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate precision scaling at the interface between unitary and non-unitary encoding under generalized noise including single-particle and collective dephasing and decay. Using linear response theory and the error propagation formula, we derive analytic precision expressions for both the unitary parameter $Ω$ and the dissipation strength $γ$. For unitary encoding, when the observable commutes with a Hermitian noise operator, the optimal encoding time is independent of $N$, yielding the Heisenberg limit $ΔΩ\propto 1 / N$; otherwise the precision degrades to the standard quantum limit or ceases to improve with $N$. For non-unitary encoding, when $[\hat{A}, \hat{O}] = 0$, the precision is insensitive to intrinsic dynamics and encoding time, scaling as $Δγ\propto \sqrt{γ/ \expval*{\hat{L}^\dagger \hat{L}}}$. Notably, for collective decay, the Dicke state reaches the Heisenberg limit $Δγ\propto 1 / N$, demonstrating that entanglement can enhance non-unitary estimation. Our results provide a unified framework and practical guidance for designing quantum metrology protocols in noisy environments.

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