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Evaluating the quantum Ziv-Zakai bound for phase estimation in noisy environments
Optics Express
|October 14, 2022
Summary
The quantum Ziv-Zakai bound (QZZB) offers better precision in noisy quantum phase estimation. This study derives an asymptotically tight QZZB, revealing how photon loss and phase diffusion impact different quantum states, guiding future research.
Area of Science:
- Quantum information science
- Quantum metrology
- Quantum estimation theory
Background:
- The quantum Ziv-Zakai bound (QZZB) is crucial for precision limits in quantum parameter estimation, especially in non-Gaussian regimes.
- Evaluating QZZB performance under environmental noise, like photon loss and phase diffusion, is challenging without approximations.
Purpose of the Study:
- Derive an asymptotically tight QZZB for phase estimation in the presence of photon loss and phase diffusion.
- Analyze the estimation performance of the QZZB for various Gaussian quantum states.
Main Methods:
- Utilized the variational method.
- Employed the technique of integration within an ordered product of operators.
- Investigated coherent states (CS), single-mode squeezed vacuum states (SMSVS), and two-mode squeezed vacuum states (TMSVS).
Main Results:
- The derived QZZB provides an asymptotically tight lower bound on precision.
- Under photon loss, coherent states exhibit better QZZB performance than squeezed states.
- For phase diffusion, the two-mode squeezed vacuum state can outperform the coherent state over a broad range of noise strengths.
Conclusions:
- The study provides an asymptotically tight QZZB for noisy quantum phase estimation.
- Different quantum states show varying resilience to photon loss and phase diffusion.
- Findings offer guidance for optimizing quantum parameter estimation in realistic, noisy environments.
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