Fisher and Skew Information Correlations of Two Coupled Trapped Ions: Intrinsic Decoherence and Lamb-Dicke Nonlinearity

It is well known that many quantum information processing methods in artificial atoms depend largely on their engineering properties and their ability to generate quantum correlations. In this paper, we investigate the non-classical correlation dynamics of two trapped ions by using local quantum Fisher information, local quantum uncertainty, as well as logarithmic negativity. The system engineering is designed such that the two-trapped-ions work as two diploe-coupled qubits in a Lamb-Dicke regime. The center-of-mass vibrational modes are initially in coherent/even coherent states. It is found that the two-trapped-ions correlations can be controlled by the Lamb-Dicke nonlinearity, the nonclassicality effect of the initial center-of-mass vibrational mode, as well as the trapped-ion coupling and the intrinsic decoherence. The sudden changes in the non-classical correlations and their stability are shown against Lamb-Dicke nonlinearity, the nonclassicality, the trapped-ion coupling, and the intrinsic decoherence.

Sequential phonon measurements of atomic motion

The motion of trapped atoms plays an essential role in quantum mechanical sensing, simulations and computing. Small disturbances of atomic vibrations are still challenging to be sensitively detected. It requires a reliable coupling between individual phonons and internal electronic levels that light can readout. As available information in a few electronic levels about the phonons is limited, the coupling needs to be sequentially repeated to further harvest the remaining information. We analyze such phonon measurements on the simplest example of the force and heating sensing using motional Fock states. We prove that two sequential measurements are sufficient to reach sensitivity to force and heating for realistic Fock states and saturate the quantum Fisher information for a small amount of force or heating. It is achieved by the conventionally available Jaynes-Cummings coupling. The achieved sensitivities are found to be better than those obtained from classical states. Further enhancements are expectable when the higher Fock state generation is improved. The result opens additional applications of sequential phonon measurements of atomic motion. This measurement scheme can also be directly applied to other bosonic systems including cavity QED and circuit QED.

Taming singularities of the quantum Fisher information

Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, forcing one away from the paradigm of regular statistical models. These questions of nonregular quantum statistical models are present in both single- and multiparameter estimation. Geometrically, singular QFIMs occur when the curvature of the metric vanishes in one or more directions in the space of probability distributions, while QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios, stressing the physical implications of singular QFIMs and the ensuing ramifications for quantum metrology.