APPPHYS 225: Probability and Quantum Mechanics

Tue+Thu 2:15-3:30pm / 126 McCollough

 

 

Syllabus

Tue 1 (9/23) Classical probability 1: random variables as functions on a sample space, matrix notation
Thu 1 (9/25) Classical probability 2: conditioning, inference/decision problems, state discrimination

Tue 2 (9/30) Quantum states/measurement as non-commutative probability; state discrimination
Thu 2 (10/2) Generalized measurement theory, optimization over POVM’s

Tue 4 (10/14) Inference-disturbance tradeoffs in quantum measurement scenarios

Tue 5 (10/21) Pure states, ensembles, superposition versus incoherent mixture, uncertainty
Thu 5 (10/23) Tensor-product structure of joint systems; joint evolution
Fri 5 (10/24) Partial projections and partial traces

Tue 6 (10/28) “Deriving” the Projection Postulate; the contingency of least-squares
Thu 6 (10/30) CHSH inequalities; classical versus quantum correlations
Fri 6 (10/31) Quantum state teleportation

Tue 7 (11/4) Entanglement of formation; entanglement of assistance
Thu 7 (11/6) No-cloning and no-broadcasting theorems
Fri 7 (11/7) Non-locality without entanglement

Tue 8 (11/11) Reference frames and super-selection rules
Thu 8 (11/13) Gisin-Popescu and “unspeakable information”
Fri 8 (11/14) Covariance with respect to symmetry groups; covariant POVM’s

Tue 9 (11/18) Dihedral symmetry and the qubit; Holevo’s construction with the Galilean group

--Thanksgiving Recess--

Tue 10 (12/2) Spekkens’ “Toy Model”
Thu 10 (12/4) Axiomatic approaches to interpretation (Hardy, Bub)

December 8-12 / Final Exams
December 16 / Grades due at noon