Quantum Information Science II, Part 1

The Bloch sphere

Quantum operations form 1: isometry + partial trace

Trace distance – bound on distinguishability of states

The Clifford group – definition and single-qubit case

Quantum opertions form 2: Kraus operator picture

The dephasing channel as depicted on the Bloch sphere

Trace norm

Quantum states and density matrices

Trace-preserving completely positive maps == Kraus rep: complete positivity

The depolarizing channel

Trace-preserving completely positive maps == Kraus rep: trace preservation

The five-qubit code – error correction

Very important fact about QEC: difference from analog computation

The five-qubit code – normalizers

What is a noisy quantum state? Introduction to density matrices