Trade-off between path entanglement and quantum sensitivity

Entanglement often increases quantum measurement schemes’ sensitivity. However, we find that in precision measurements with zero-mean Gaussian states, such as squeezed states, entanglement between different paths degrades measurement sensitivity. We prove an inverse relationship between entanglement entropy and sensitivity for measurements of single-mode phase shifts in multimode systems and for phase shifts on both modes in two-mode systems. In the two-mode case, which models devices such as interferometers, we find that entanglement strongly degrades differential phase sensitivity. Finally, we show that minimizing entanglement between paths maximizes the phase sensitivity of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>N</a:mi></a:math>-mode systems with zero-mean Gaussian state inputs.