Quantum sensors based on weak-value amplification cannot overcome decoherence

Sensors that harness exclusively quantum phenomena (such as entanglement) can achieve superior performance compared to those employing only classical principles. Recently, a technique based on postselected, weakly performed measurements has emerged as a method of overcoming technical noise in the detection and estimation of small interaction parameters, particularly in optical systems. The question of which other types of noise may be combated remains open. We here analyze whether the effect can overcome decoherence in a typical field-sensing scenario. Benchmarking a weak, postselected measurement strategy against a strong, direct strategy, we conclude that no advantage is achievable, and that even a small amount of decoherence proves catastrophic to the weak-value amplification technique.