Quantum metrology with entangled coherent states (1101.5044v3)

Abstract: We present an improved phase estimation scheme employing entangled coherent states and demon- strate that the states give the smallest variance in the phase parameter in comparison to NOON, BAT and "optimal" states under perfect and lossy conditions. As these advantages emerge for very modest particle numbers, the optical version of entangled coherent state metrology is achievable with current technology.

• The paper demonstrates that entangled coherent states achieve lower phase uncertainty than NOON and BAT states across varying loss regimes.
• The paper employs quantum Fisher information and modest photon numbers to quantify enhanced precision in realistic optical setups.
• The paper highlights practical implications for quantum metrology by showcasing ECS's robustness to particle loss compared to traditional states.

An Examination of Quantum Metrology with Entangled Coherent States

The paper "Quantum Metrology with Entangled Coherent States" by Jaewoo Joo, William J. Munro, and Timothy P. Spiller presents an advanced exploration into the use of entangled coherent states (ECS) for phase estimation, a critical aspect of quantum metrology. This research is situated within the broader context of leveraging modest quantum resources to achieve quantum advantage—a pertinent endeavor given the current constraints on realizing large-scale quantum computing technologies.

Overview and Numerical Results

The authors propose and demonstrate that ECS can achieve the smallest variance in the phase parameter compared to NOON, BAT, and what are often designated as "optimal" states, even under lossy conditions. Notably, ECS show significant advantages with very modest particle numbers, asserting that optical implementations using ECS could be practical with existing technology. A stark comparison against NOON states is established, particularly emphasizing ECS's robustness to particle loss—a critical factor for practical applications in quantum metrology since NOON states suffer quickly in efficacy due to their fragility in the presence of particle loss.

By calculating the quantum Fisher information, which provides a metric for the precision of quantum phase measurements, the authors quantify the phase uncertainty across different states in a variety of scenarios (lossless, weak, moderate, and high loss regimes). The ECS outperforms others when using the same average particle number both under ideal and lossy conditions, making ECS a superior choice in multiple contexts. Specifically, for modest photon-numbers, such as $N=4$ and $\alpha=2$, the ECS advantage is highlighted through calculated phase uncertainties. The results show that ECS not only overshadow NOON and BAT states but continue to maintain their strength relative to uncorrelated states as transmission rates decrease.

Theoretical and Practical Implications

The potential implications of this research in quantum technologies cannot be overstated. From a theoretical perspective, the demonstrated robustness and effectiveness of ECS in phase estimation provide deeper insights into the quantum-classical boundaries and the practical realization of quantum advantages. ECS's ability to act as a superposition of NOON states with varying photon numbers, besides their resilience to decoherence, presents a marked improvement in realizing practical quantum metrology applications over more traditional methods.

Practically, the feasibility of preparing a traveling Schrödinger-cat state as a prerequisite for generating ECS is encouraging. The authors propose that with existing optical setups, particular configurations incorporating beam splitters and parity measurements could realize these ECS to leverage their phase estimation benefits. Moreover, the analysis suggests that while NOON states tend to be optimal in high transmission scenarios, ECS provide a continuous advantage even as conditions degrade, making them attractive for near-term implementation in real-world settings.

Future Directions

Explorations into optimizing ECS generation, coupled with investigating the synergistic effects of introducing squeezed states and other non-linear elements within the metrological setups, represent promising future directions. Moreover, further empirical validations using current optical technologies could offer pathways toward scalable deployment in quantum sensing and related applications.

In conclusion, this critical examination by Joo, Munro, and Spiller solidifies ECS's role as a formidable tool in quantum metrology. As quantum technologies continue to mature, the principles and findings expounded in this paper lay down a solid foundation for continued exploration of quantum entangled states, paving the way for future innovations and applications within quantum measurement science.