Physics / advanced
Quantum information and entanglement
Analyze quantum correlations and communication resources through operational tasks, entropy inequalities, distinguishability, and well-defined information protocols.
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Module 01 advanced
Quantum information and entanglement
Analyze quantum correlations and communication resources through operational tasks, entropy inequalities, distinguishability, and well-defined information protocols.
- 01
Trace distance and state discrimination
Turn a difference of density operators into an optimal binary decision and distinguish measurement limitations from preparation uncertainty.
27 min - 02
Fidelity and Bures distance
Separate squared fidelity from root fidelity and connect overlaps, purification geometry, and operational distance bounds.
27 min - 03
Von Neumann entropy and purification
Compute entropy from spectra and use an explicit tensor factor and partial trace to distinguish local uncertainty from global mixedness.
27 min - 04
Mutual information and relative entropy
Quantify total correlations with relative entropy and derive the direction and assumptions of quantum data processing.
27 min - 05
Bell–CHSH tests and local hidden variables
Derive a Bell bound from local response functions and identify the experimental assumptions needed to turn correlations into a valid test.
27 min - 06
Entanglement witnesses and separability
Use convexity and Bell-state overlap to certify entanglement while respecting the one-sided nature of a witness.
27 min - 07
Quantum teleportation resource accounting
Track Bell-measurement branches, Pauli corrections, and the separate entanglement and classical communication resources of teleportation.
27 min - 08
Superdense coding and classical capacity
Encode four orthogonal joint states with one transmitted qubit and reconcile the protocol with the Holevo bound by counting shared entanglement.
27 min - 09
No-cloning and no-broadcasting theorems
Prove deterministic no-cloning from preserved inner products and distinguish independent copies from correlated broadcasting of commuting states.
27 min - 10
Quantum channel capacities and coding limits
Define communication rates with explicit assistance and use the flagged erasure channel to separate classical, quantum, and two-way-assisted transmission.
27 min