Quantum-enhanced protocols : secure quantum state sharing and noisy field estimation

The first part of this thesis presents a new quantum state sharing scheme that distributes the quantum information contained within a quantum state across three shares such that it cannot be accessed from any individual share. By combining any two shares, however, the original state can be reconstructed. This requirement for collaboration ensures security against single dishonest actors. We demonstrate that the protocol is provably secure for the class of pure Gaussian states and is effective for the sharing of mixed states, although security for those cannot be guaranteed. We then go on to discuss the use of quantum state sharing as a hybrid protocol for the distribution of discrete-variable states, including Fock states and particle-number qubits, using Gaussian entanglement. We demonstrate that, with access to suitable entanglement resources, this can be achieved with arbitrarily-high fidelity and that the security of the protocol can be guaranteed for qubit-like states. In the second part of this thesis, we consider the potential for quantum entanglement to improve the measurement of gradients in the magnetic field. We find that in the absence of noise, it is optimal to measure orthogonal gradients individually, devoting the full measurement network to the measurement of a single gradient at a time. In the presence of high levels of environment noise, however, it becomes preferable to measure them simultaneously. We find the optimal network configurations and entanglement structures to make these measurements in the presence of three common noise sources.