Fidelity Bounds for Device-Independent Advantage Distillation

Abstract

Low noise tolerances for current device-independent quantum key distribution protocols and the existence of fidelity-related security conditions in device-independent advantage distillation motivate the need for strong lower bounds on the fidelity. This thesis shows that a reduction to qubits does not deliver optimal bounds. An algorithm is derived that can in principle bound the fidelity for our device-independent setup to an arbitrary precision. This algorithm is computable with a semi-definite program and a constraint optimization. We conclude with a conjecture for a necessary security condition against collective attacks, where a repetition-code protocol that applies advantage distillation is considered.