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Precision measurements of optical phases have many applications in science and technology. Entangled multi-photon states have been suggested for performing such measurements with precision that significantly surpasses the shot-noise limit.…
Precise measurements are the key to advances in all fields of science. Quantum entanglement shows higher sensitivity than achievable by classical methods. Most physical quantities including position, displacement, distance, angle, and…
Phase measurement using a lossless Mach-Zehnder interferometer with certain entangled $N$-photon states can lead to a phase sensitivity of the order of 1/N, the Heisenberg limit. However, previously considered output measurement schemes are…
Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific…
Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used the quantum Fisher…
Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration and optical path length. Quantum entanglement enables higher…
We construct a projection measurement process for the maximally entangled N-photon state (the NOON-state) with only linear optical elements and photodetectors. This measurement process will give null result for any N-photon state that is…
Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit. However, the N-photon parity measurements required to achieve this optimal sensitivity…
When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate…
Entangled multi-photon states have the potential to provide improved measurement accuracy, but are sensitive to photon loss. It is possible to calculate ideal loss-resistant states that maximize the Fisher information, but it is unclear how…
A measurement process is constructed to project an arbitrary two-mode $N$-photon state to a maximally entangled $N$-photon state (the {\it NOON}-state). The result of this projection measurement shows a typical interference fringe with an…
We present an improved phase estimation scheme employing entangled coherent states and demon- strate that the states give the smallest variance in the phase parameter in comparison to NOON, BAT and "optimal" states under perfect and lossy…
To acquire the best path-entangled photon Fock states for robust quantum optical metrology with parity detection, we calculate phase information from a lossy interferometer by using twin entangled Fock states. We show that (a) when loss is…
A method for exploring photon-number entangled states with weak nonlinearities is described. We show that it is possible to create and detect such entanglement at various scales, ranging from microscopic to macroscopic systems. In the…
Multi-mode NOON states can quantum-enhance multiple-phase estimation in the absence of photon loss. However, a multi-mode NOON state is known to be vulnerable to photon loss, and its quantum-enhancement can be dissipated by lossy…
For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states,…
We experimentally demonstrate a general criterion to identify entangled states useful for the estimation of an unknown phase shift with a sensitivity higher than the shot-noise limit. We show how to exploit this entanglement on the examples…
Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was…
Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the…
Given a non-maximally entangled state, an operationally significant question is to quantitatively assess as to what extent the state is away from the maximally entangled state, which is of importance in evaluating the efficacy of the state…