The advent of increasingly precise gyroscopes has played a key role in the technological development of navigation systems. Ring-laser and fiber-optic gyroscopes, for example, are widely used in modern inertial guidance systems and rely on the interference of unentangled photons to measure mechanical rotation. The sensitivity of these devices scales with the number of particles used as 1/ √ N . Here we demonstrate how, by using sources of entangled particles, it is possible to do better and even achieve the ultimate limit allowed by quantum mechanics where the precision scales as 1/N. We propose a gyroscope scheme that uses ultracold atoms trapped in an optical ring potential.

We describe a scheme to demonstrate the nonlocal properties of a single particle by showing a violation of Bell's inequality. The scheme is experimentally achievable as the only inputs are number states and mixed states, which serve as references to 'keep track of the experiment'. These reference states are created completely independently of one another and correlated only after all the measurement results have been recorded. This means that any observed nonlocality must solely be due to the single particle state. All the techniques used are equally applicable to massive particles as to photons and as such this scheme could be used to show the nonlocality of atoms.

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By exploiting the correlation properties of ultracold atoms in a multimode interferometer, we show how quantum enhanced measurement precision can be achieved with strong robustness to particle loss. While the potential for enhanced measurement precision is limited for even moderate loss in two-mode schemes, multimode schemes can be more robust. A ring interferometer for sensing rotational motion with noninteracting fermionic atoms can realize an uncertainty scaling of 1/(N√η) for N particles with a fraction η remaining after loss, which undercuts the shot-noise limit of two-mode interferometers. A second scheme with strongly interacting bosons achieves a comparable measurement precision and improved readout.

We present a practical scheme for measuring completely unknown phases with a precision beyond the shot-noise limit even in the presence of loss. Our scheme consists of sending a sequence of unentangled particles and NOON states through an interferometer and analyzing the measurement outcomes using a Bayesian analysis. We compare our results with two recent schemes [L. Pezzé and A. Smerzi, Europhys. Lett. 78, 30004 (2007); B. L. Higgins et al., Nature (London) 450, 393 (2007)] that are closely related but operate in the lossless regime. We show that our technique outperforms the previous schemes when even a modest amount of loss is present and so may prove to be a valuable technique for making precision measurements beyond the classical limit in a range of practical scenarios.