Noiseless linear amplification-based quantum Ziv-Zakai bound for phase estimation and its Heisenberg error limits in noisy scenarios

TL;DR

This paper investigates how noiseless linear amplification enhances phase estimation precision in noisy quantum scenarios, deriving new Heisenberg error bounds and demonstrating significant performance improvements, especially under severe photon loss.

Contribution

It introduces NLA-based techniques within the quantum Ziv-Zakai bound framework to improve phase estimation in noisy environments and derives new Heisenberg error limits surpassing traditional bounds.

Findings

NLA significantly improves phase estimation in noisy scenarios.

Performance enhancement is more pronounced with severe photon loss.

New Heisenberg error bounds outperform traditional bounds in minimal loss cases.

Abstract

In this work, we address the central problem about how to effectively find the available precision limit of unknown parameters. In the framework of the quantum Ziv-Zakai bound (QZZB), we employ noiseless linear amplification (NLA)techniques to an initial coherent state (CS) as the probe state, and focus on whether the phase estimation performance is improved significantly in noisy scenarios, involving the photon-loss and phase-diffusion cases. More importantly, we also obtain two kinds of Heisenberg error limits of the QZZB with the NLA-based CS in these noisy scenarios, making comparisons with both the Margolus-Levitin (ML) type bound and the Mandelstam-Tamm (MT) type bound. Our analytical results show that in cases of photon loss and phase diffusion, the phase estimation performance of the QZZB can be improved remarkably by increasing the NLA gain factor. Particularly, the improvement is more pronounced with severe photon losses. Furthermore in minimal photon losses, our Heisenberg error limit shows better compactness than the cases of the ML-type and MT-type bounds. Our findings will provide an useful guidance for accomplishing more complex quantum information processing tasks.