Pushing measurements to their limits and beyond: A quantum receiver that beats the standard quantum limit
Measurement is at the heart of quantum mechanics, and quantum mechanics sets limits on how well we can measure the state of a physical system. For example, nonorthogonal states, such as coherent states, cannot be perfectly distinguished by any deterministic measurement due to their intrinsic overlap. The minimum error in discriminating nonorthogonal states using an ideal conventional measurement of the physical property that differentiates these states, such as a heterodyne measurement, is given by the standard quantum limit (SQL). This limit bounds the ultimate performance of existing coherent communications and many coherent-state-based quantum information protocols as well. But there are ways of measuring coherent states that can beat this limit and achieve even lower errors. Such schemes have been sought for many years, with results providing only marginal improvements beyond the standard quantum limit. Moving into a new regime, we have implemented a quantum receiver that discriminates four nonorthogonal coherent states with error probabilities below the SQL for a wide range of input powers, and that reaches error probabilities 6 dB below the SQL.