Protein NMR Limit

1. **Brief critique and context**: The "Protein NMR Limit" conjecture addresses the current technological and methodological barriers in using diamond nitrogen-vacancy (NV) center sensors for resolving nuclear magnetic resonance (NMR) signals from a single protein molecule at room temperature and ambient conditions. The main challenges include achieving sufficient sensitivity and resolution at the single-molecule level, dealing with noise and environmental disturbances, and the inherently weak magnetic field signals from single nuclei. While NV centers have shown promise due to their high sensitivity and non-invasive nature, overcoming these limitations remains a significant hurdle in the field of quantum sensing and NMR spectroscopy.

2. **Recent research**: Recent advancements have been made in the sensitivity and spatial resolution of NV center sensors. A study by Schwartz et al. (2021) demonstrated enhanced sensitivity to weak magnetic fields using advanced quantum control techniques. Another study by Lovchinsky et al. (2016) showed the potential for NV centers to detect individual nuclear spins in proteins, albeit under non-ambient conditions. These advancements suggest progress towards overcoming the limitations highlighted in the conjecture. See: https://www.nature.com/articles/s41565-020-00784-7 and https://www.science.org/doi/10.1126/science.aad8022.

3. **Bayesian likelihood of falsification (with reasoning)**: The Bayesian likelihood of this conjecture being falsified within 5 years is approximately 40%. While significant technological advancements are being made, achieving the required sensitivity and resolution under ambient conditions remains challenging. The current trajectory of research suggests incremental improvements, but a breakthrough sufficient to meet the conjecture's criteria within five years is uncertain, though not impossible, given the pace of innovation in quantum sensing technologies.