Entangled Quantum Dynamics

This thesis addresses the connections between quantum entanglement and quantum dynamics. The central theme is that there is a resource contained in interactions between quantum systems, as described by Hamiltonians, Unitary operators and measurements, that can be classified and quantified in a similar way to entanglement in quantum states. In particular, the problem of using an interaction Hamiltonian to simulate the action of another Hamiltonian efficiently via local operations is addressed and, for two qubits, the results can be conveniently summarized by a majorization-like partial order on the space of Hamiltonians. Secondly, the relationship between interaction resources and entanglement is analyzed by considering the ability of a unitary operator to generate entanglement. Analytic results are presented for the case of a single application of a two-qubit unitary where the system acted upon is not entangled to any ancillary systems. Numerical results are presented for the case where such ancillas are present. The notion of processing multiple copies of a unitary operator collectively is discussed and is shown to be unnecessary for generating the maximum amount of entanglement per application of the operation. Finally, a different kind of connection between dynamics and entanglement is investigated by finding ways in which the entanglement properties of unknown, multiparty quantum states can be determined efficiently by measurements on multiple copies of the state. Specifically, networks for directly measuring invariants under local unitary transformations and stochastic local operations and classical communication are presented and their efficiency is compared to alternative methods based on estimating the coefficients of the state.