Estimating a completely unknown initial phase of a Quantum State of light with ultra-high precision using an adaptive measurement scheme.

Quantum Phase Estimation is an important part of Quantum Metrology since it may have potential applications within field as Quantum Information and Quantum Computation. Imprinting information on the phase, it's crucial that one may estimate the phase on the receiving side as good as possible – i.e. limited only by quantum noise.

Estimating the phase of a completely unknown quantum state – say, a simple coherent state - is usually done by heterodyne measurement. In such a standard measurement both the unknown coherent amplitude and initial phase is measured. Seen from an informational point of view, Quantum Mechanics offers no free lunch and we must pay the penalty of twice the amount of noise – or uncertainty - in the measurement, than there should have been if we could have measured the phase alone. In this sense the standard heterodyne measurement is not optimal.

Interestingly, if we had known the initial phase of the quantum state we may just have turned the quantum state orthogonal to the strong reference beam in a homodyne measurement and obtained a quantum-noise-limited phase measurement. Unfortunately, since we have no prior knowledge about the initial phase, this is not a viable path. However, we could use fast heterodyne measurements in the beginning of the measurement to accumulate a rough phase estimate and then turn the quantum state orthogonal to the reference beam towards the end and finish in a homodyne measurement scheme.

Using such an adaptive homodyne measurement scheme it has been shown that it is possible to circumvent the imperfection of the heterodyne measurement scheme and reach a quantum-noise-limited phase measurement [see Wiseman, Phys. Rev. Lett. 75, 4587 (1995)].

We are trying to implement this specific scheme and other kinds of adaptive phase measurement schemes experimentally using Quantum Optics and state-of-the-art optical technologies.

- Clemens Schäfermeier
- (formerly) Adriano Berni
- (formerly) Bo Melholt Nielsen
- Ulrik Lund Andersen