Abstract High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.
Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary
Uφ happen simultaneously) without using more applications of
Uφ, albeit at the expense of using many more qubits. It is also known that there is no advantage for adaptive algorithms in the case where the phase that needs to be estimated is arbitrary or is uniformly random. Here we give examples of a special case of phase estimation, with a promise on the values that the unknown phase can take, where adaptive methods are provably better than non-adaptive methods by a factor of nearly 2 in the number of uses of
Uφ. We also prove some upper bounds on the maximum advantage that adaptive algorithms for phase estimation can achieve over non-adaptive ones.
Quantum parameter estimation exploits quantum states to achieve estimation sensitivity beyond classical limit. In continuous variable (CV) regime, squeezed state has been exploited to implement deterministic phase estimation. It is however, often restricted by fragility of quantum states. The quantum phase estimation sensitivity of squeezed state is significantly affected by loss or detection inefficiency, which restrict its applications. This issue can be solved by using a method of parametric amplification of squeezed state \cite{OPA}. In this work, we implement multi-phase estimation with optical parametric amplification of entanglement generated from squeezed states. We find multi-phase estimation sensitivity is robust against loss or detection inefficiency, where we use two-mode Einstein-Podolsky-Rosen entangled state and four-mode cluster state for analysis. Our work provides a method for realizing large-scale quantum metrology in real-world applications against loss or detection inefficiency.