Practical quantum limit of linear waveform estimation via local oscillator modulation

The Holevo Cramer Rao bound (HCRB) sets the fundamental limit for multi-parameter estimation for non-commuting observables, as is generally the case when classical signals are encoded in linear quantum noise-limited sensors, such as gravitational-wave interferometers. It has been recently established that by passing the output signal field into a set of detuned squeezers, then performing joint homodyne and heterodyne measurements, the HCRB could be attained in the limit of infinite squeezing. However, this scheme is cumbersome and difficult to implement in practice. 

In this work, we provide a much simpler scheme which relies on a single balanced detector and a modulated local oscillator, which achieves near-HCRB performance. By optimizing the spectral shape of the local oscillator, our scheme approximates the HCRB down to ~3% of extra relative error. We theoretically justify this gap by providing novel insights into the attainability of the HCRB in practical measurement schemes, where only a subset of all possible measurements can be explored. Our proposed scheme requires minimal hardware and can be readily implemented in quantum-limited optomechanical systems such as LIGO or fiber-optic communication, where signals are contained in spectral quadratures of the electromagnetic field.