| Topic | Readings | Notes | |
| Lecture #1 (01/08) |
Overview of Quantum Information Science Review of Linear Algebra |
NC pages 61 - 79 |
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| Lecture #2 (01/10) |
Review of Linear Algebra Introduction to Quantum Mechanics |
NC pages 80 - 96 and 98 - 111 |
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| Lecture #3 (01/15) |
Schmidt Decomposition Density Operators Reduced Density Operators Purifications |
NC pages 356 - 373 and 84 - 92 |
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| Lecture #4 (01/17) |
Quantum Operations POVM Measurements Generalized Measurements Introduction to Shannon Entropy and von Neuman Entropy Joint Entropy Conditional Entropy Relative Entropy Mutual Information |
NC Chapter 11 |
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| Lecture #5 (01/22) |
Klein's Inequality Joint Entropy Theorem Subadditivity Triangle Inequality Concativity Strong Subadditivity and its consequences etc. |
NC page 86 and pages 528 - 535 |
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| Lecture #6 (01/24) |
Classical and Quantum Data Processing Inequalities Indistinguishability of Quantum States and the No-Cloning Theorem Accessible Information and the Holevo Bound |
NC Chapter 9 | |
| Lecture #7 (01/29) |
Applications of the Holevo bound Fano's inequality and the Quantum Fano inequality The Trace Distance and it's properties |
NC Chapter 9 | |
| Lecture #8 (01/31) |
Fidelity and it's properties Relationships between the trace distance and fidelity Continuity of entropy(Fannes's inequality) Ensemble average fidelity and the entanglement fidelity |
NC pages 536-542 | |
| Lecture #9 (02/05) |
Properties of the entanglement fidelity Revisiting the quantum Fano inequality Quantum teleportation and superdense coding Entanglement distillation and dilution Introduction to classical data compression |
NC Pages 542-546 and the solutions to Problem Set #1 | |
| Lecture #10 (02/07) |
The Chebyshev inequality The law of large numbers The theorem of typical sequences Proof of the noisy channel coding theorem |
NC Pages 542-546 and 578-580 | |
| Lecture #11 (02/12) | Quantum data compression | NC Pages 578-580 | |
| Lecture #12 (02/14) | Revisiting entanglement distillation and dilution | ||
| Lecture #13 (02/19) |
Overview of noiseless quantum Shannon theory Trade-offs in blind data compression Description of the mostgeneral problem in visible data compression (generalized remote state preparation) |
Pages 1-7 of Anura's thesis | |
| Lecture #14 (02/26) | Trade-off coding and the the Quantum-Classical trade-off | Pages 1-7 and 23-31of Anura's thesis | |
| Lecture #15 (02/28) |
Conditionally typical projectors Frequency typical sequences Properties of frequency typical projectors |
Coding theorems and strong converse for quantum channels-Andreas Winter IEEE Vol.45,No.7 | |
| Lecture #16 (03/04) | The Father Protocol of noiselss quantum Shannon theory (one shot eSDC) | ||
| Lecture #17 (03/06) | The Father Protocol continued | ||
| Lecture #18 (03/18) |
Optimality of one-shot eSDC and eRSP Ensemble version of eSDC |
Pages 29-31 and 31-40 of Anura's thesis | |
| Lecture #19 (03/20) | Generalized remote state preparation | Pages 190-197 of Elements of Information Theory- Cover and Thomas | |
| Lecture #20 (03/25) |
Overview of classical noisy channel coding The theorem of jointly typical sequences |
Pages 198-203 of Elements of Information Theory- Cover and Thomas | |
| Lecture #21 (03/27) | Noisy Channel Coding | ||
| Lecture #22 (04/01) |
Noisy Channel Coding continued Source Channel Coding Overview of sending classical information over noisy quantum channels |
NC pages 554-557 | |
| Lecture #23 (04/03) | Classical information over noisy quantum channels | NC page 558 | |
| Lecture #24 (04/08) |
The additivity questions in QIT Optimality of the product state capacity |
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| Lecture #25 (04/10) |
Optimality of the product state capacity continued The fundamental tasks of QIT |
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| Lecture #26 (04/15) |
The QIT family tree The Fully Quantum Slepian Wolf protocol (FQSW) |
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| Lecture #27 (04/17) | Obtaining the other protocols from FQSW |
| Student | Topic |
| Amy Thompson | Quantum Cryptography |
| Diego Valente | Coherent Classical Communication |
| Chen-Fu Chiang | On quantum capacity of erasure channel assisted by back classical communication |
| Hamed Ahmadi | Equivalence of additivity questions in quantum information theory |