Quantum squeezing cannot beat the standard quantum limit

Abstract: Quantum entanglement between particles is expected to allow one to perform tasks that would otherwise be impossible. In quantum sensing and metrology, entanglement is often claimed to enable a precision that cannot be attained with the same number of particles and time, forgoing entanglement. Two distinct approaches exist: creation of entangled states that either i) respond quicker to the signal, or ii) are associated with lower noise and uncertainty. The second class of states are generally called squeezed states. Here we show that if our definition of success is -- a precision that is impossible to achieve using the same resources but without entanglement -- then the second approach cannot succeed. In doing so we show that a single non-separable squeezed state provides fundamentally no better precision, per unit time, than a single particle.