QCQI – Chapter 10: Entanglement, Entropy & Information Tasks

Course Slides (MSU)

Learning Objectives¶

• $S(\rho)$, $I(A{:}B)$, $S(A|B)$; SSA and friends.

• LOCC conversions: majorization; concentration/dilution; distillation.

• Teleportation, dense coding, swapping.

Entropy Landscape¶

SSA: $I(A{:}C|B)\ge 0$; $S(A|B)$ can be $<0$.

Eureka! Negative conditional entropy is an entanglement witness.

Pure-State Entanglement¶

Schmidt coefficients $\lambda_i$ ; rate $=H(\lambda)$ for concentration/dilution.

Eureka! Entanglement of a pure state equals its local entropy.

Mixed-State Measures¶

Two-qubit concurrence $\to E_F$; PPT $\to$ negativity; note PPT$\not\Rightarrow$ separable in higher dims.

Information Tasks¶

Teleportation (Bell meas. + Pauli), Dense coding (Pauli encodings + Bell meas.), Swapping.

Schematics (concept)¶

Hands-on Notebook¶

Companion notebook (multi-backend): L14_QCQI_Ch10_Entanglement_Entropy_and_Information_Tasks

Set backend in the first cell to cirq, pennylane, braket, pyquil, or qiskit.

Mini-Lab¶

• Verify entropy inequalities numerically.

• Concurrence vs. negativity ordering.

• One-round BBPSSW on Werner states.