Quantum Information Science: Quantum information science has numerous applications and will deeply impact our lives. By bringing methodologies from the disciplines of engineering and mathematics, we have made contributions in different aspects of efficient quantum communication. Specific contributions include:
- Quantum Entanglement Distillation: Quantum entanglement serves as a valuable resource for many important quantum operations, but in practice, the deterioration of entanglement is inevitable since the noise inherent in the channel contaminates the qubit. We have put forth quantum entanglement distillation algorithms that adapt to the quantum channel to tackle the efficiency issue. The proposed algorithms have guaranteed convergence for quantum channels with two Kraus operators, which include phase-damping and amplitude-damping channels.
- Quantum Error Correction: Quantum error correction efforts to date have generally focused on generic noise models, and thus generic error recovery procedures. Our contributions have examined the benefits of quantum error recovery (QER) tailored to a specific noise model. Specific contributions include: Demonstrated that using entanglement fidelity as the measure of performance, the optimum QER operation can be computed as the result of a semidefinite program (SDP). In this way, for any given noise model and encoding, the optimum recovery can be computed. Demonstrated the utility of eigen-analysis in interpreting and deriving QER techniques. Developed an eigenvector-based algorithm to approximate the optimum QER operation for high dimensional channels (for which computing the optimum via a SDP is computationally burdensome).