Non-Hermitian Quantum Metrology Enhancement and Skin Effect Suppression in PT-Symmetric Bardeen-Cooper-Schrieffer Chains
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911095274340352 |
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| author | Matkar, Harshank |
| author_facet | Matkar, Harshank |
| contents | We outline a theoretical framework for quantum metrology in non-Hermitian systems, demonstrating both significant failure and exceptional regimes in PT-symmetric Bardeen-Cooper-Schrieffer chains. Through biorthogonal quantum Fisher information analysis, we identify two distinct regimes: exponential sensitivity suppression in the non-Hermitian skin effect phase ($F_Q \propto N^3 e^{-2κN}$) where eigenstates localize exponentially, and quadratic enhancement near PT-breaking exceptional points [1-4] ($F_Q \propto N^2/δ$) achieving Heisenberg scaling. Our multiparameter analysis establishes optimal simultaneous estimation of chemical potential, Peierls phase, and gain/loss strength with quantum Fisher information matrix scaling as $N^2$, surpassing the standard quantum limit by factors exceeding $10^2$. For realistic parameters ($t/2π=10$ MHz, $Δ/2π=1$ MHz, $N=50$), we predict enhancement factors $η_μ\approx 20\sqrt{N}=141$ for chemical potential estimation and $η_ϕ\approx t^2 \sqrt{3N/2}=100\sqrt{N}$ over classical sensing. These results are validated through exact finite-size calculations and provide concrete protocols for superconducting circuit implementations.We reveal a core dichotomy in non-Hermitian quantum metrology: NHSE suppresses sensitivity exponentially, while $\mathcal{PT}$-symmetry enables Heisenberg-limited enhancement -- each arising from distinct spectral and localization topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Quantum Metrology Enhancement and Skin Effect Suppression in PT-Symmetric Bardeen-Cooper-Schrieffer Chains Matkar, Harshank Quantum Physics 81Q12 (Primary) 81P15, 81V70 (Secondary) We outline a theoretical framework for quantum metrology in non-Hermitian systems, demonstrating both significant failure and exceptional regimes in PT-symmetric Bardeen-Cooper-Schrieffer chains. Through biorthogonal quantum Fisher information analysis, we identify two distinct regimes: exponential sensitivity suppression in the non-Hermitian skin effect phase ($F_Q \propto N^3 e^{-2κN}$) where eigenstates localize exponentially, and quadratic enhancement near PT-breaking exceptional points [1-4] ($F_Q \propto N^2/δ$) achieving Heisenberg scaling. Our multiparameter analysis establishes optimal simultaneous estimation of chemical potential, Peierls phase, and gain/loss strength with quantum Fisher information matrix scaling as $N^2$, surpassing the standard quantum limit by factors exceeding $10^2$. For realistic parameters ($t/2π=10$ MHz, $Δ/2π=1$ MHz, $N=50$), we predict enhancement factors $η_μ\approx 20\sqrt{N}=141$ for chemical potential estimation and $η_ϕ\approx t^2 \sqrt{3N/2}=100\sqrt{N}$ over classical sensing. These results are validated through exact finite-size calculations and provide concrete protocols for superconducting circuit implementations.We reveal a core dichotomy in non-Hermitian quantum metrology: NHSE suppresses sensitivity exponentially, while $\mathcal{PT}$-symmetry enables Heisenberg-limited enhancement -- each arising from distinct spectral and localization topologies. |
| title | Non-Hermitian Quantum Metrology Enhancement and Skin Effect Suppression in PT-Symmetric Bardeen-Cooper-Schrieffer Chains |
| topic | Quantum Physics 81Q12 (Primary) 81P15, 81V70 (Secondary) |
| url | https://arxiv.org/abs/2508.04815 |