Quantum Information Science II, Part 1

• Introduction to quantum information science
• Quantum states and operations - overview
• Density matrices and ensembles
• Mathematical definition of density matrices
• Special cases of density matrices - pure states
• Special cases of density matrices - probability distributions
• Eigenvalues of density matrices specify a probability distribution
• Special cases of density matrices - qubits
• The Bloch sphere
• Deterministic classical and quantum maps
• Classical random maps
• Introduction to quantum operations
• What is a noisy quantum state? Introduction to density matrices
• Indistinguishability of density matrix ensemble unravelings
• Measurements and density matrices
• Action of unitary transform on density matrices
• Effect of measurement on an ensemble of states
• Density matrix properties
• Density matrices and the partial trace - example
• Density matrices and the partial trace - definition
• Equivalence of density matrices to partial trace computed in different bases
• Bloch sphere representation of single qubit density matrix states
• Quantum mechanics and quantum circuits
• Density matrices
• Overview - Three representations of quantum operations