CREATING, DESTROYING AND PRESERVING COHERENCE WITH QUANTUM CHANNELS

Author

Masaya Takahashi, Southern Illinois University CarbondaleFollow

Date of Award

5-1-2022

Degree Name

Doctor of Philosophy

Department

Physics

First Advisor

Byrd, Mark

Abstract

Quantum coherence is a fundamental property of quantum systems that can be studied within the framework of a quantum resource theory. In chapter 2, we consider how much coherence can be either generated or destroyed on a bipartite system when the action is restricted to local unitary operations. For pure states, we find that the relative entropy of entanglement and the robustness of entanglement provide tight lower bounds on the amount of coherence that can be destroyed by local unitaries, as measured by the relative entropy and L1 measures of coherence, respectively. We then study the amount of bipartite pure entanglement that can be either maximized or minimized when the action is restricted to a global incoherent operation. For two-qubit pure states, maximum and minimum are shown in terms of coefficients of given state with incoherent basis. In chapter 3, we study optimal ways to create a large amount of quantum coherence via quantum channels. For this, we compare different scenarios, where the channel is acting on an incoherent state, on states which have coherence, and also on subsystems of multipartite quantum states. We show that correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We also study the ability of quantum channels to destroy coherence, proving that a channel can destroy more coherence when acting on a subsystem of a bipartite state. Crucially, we also show that the destroyed coherence on multipartite system can exceed the upper bound of those on the single system when the total state is entangled. Our results significantly simplify the evaluation of coherence generating capacity of quantum channels, which we also discuss.In chapter 4, We study a protocol to preserve coherence against error. Our approach is to discretize the state change caused by error into bit flip or phase flip which do not cause any coherence change by the parity check measurement. We show a two qubits code preserving coherence against the collective Hadamard gate.