
Instructor  Dominique Unruh 
TA  RaulMartin Rebane (submit homework solutions here) 
Lecture Period  February 10  May 26 
Lectures  Wednesdays, 16:1517:45, Zoom (link in Slack chat)
(Dominique; may sometimes be switched with tutorial) 
Practice sessions 
Tuesdays, 16:1517:45, Zoom (link in Slack chat) (RaulMartin) 
Slack  https://quantumcrypto2021.slack.com/ 
Course Material  Lecture
notes (old ones), blackboard photos, practice blackboard photos, and exam study guide. 
Language  English 
Exam  May 30, 12:00 – 15:00. (Reexam will be scheduled later.) 
Contact  Dominique Unruh <<surname> at ut dot ee> 
Date  Summary  Knowlets covered  Materials 

Feb 10  Quantum systems, quantum states, unitary operations.  QState, UniTrafo, PauliX  Video, Whiteboard 
Feb 16  Small exercises with single qubits. Polarization invariant under rotation.  QState, UniTrafo, Hada, Rota  Whiteboard 
Feb 17  Measurements in computational basis. ElitzurVaidman bomb tester. Complete measurements.  CBMeas, Bomb, ComplMeas, CompBasis  Video, Whiteboard 
Feb 23  Light filters as measurements. Improved bomb tester. Quantum Zero effect.  Bomb, ComplMeas  Whiteboard 
Mar 02  Initializing using measurements. States from prob. distributions. Equivalent definitions of unitary.  ComplMeas, ConjTrans, Dirac  Whiteboard 
Mar 03  Projective measurements. Tensor product. Composition of quantum systems / quantum states / unitaries / measurements.  ProjMeas, ProjMeasVS, ComposQSys, ComposQState, Tensor, ComposUni, ComposMeas  Video, Whiteboard 
Mar 09  Using tensor product and proj. measurements. Quantum teleportation.  ProjMeas, Tensor, ComposUni, ComposMeas  Whiteboard 
Mar 10  Deutsch's algorithm. Quantum state probability distributions (ensembles). Operations on ensembles. Density operators.  Deutsch, QDistr, PhysInd, QDistrU, QDistrX, QDistrM, Density  Video, Whiteboard 
Mar 16  Distinguishing incorrect toy crypto. Density operators. Creating unitaries for boolean functions.  QDistr, QDistrM, Density, DensityPhysInd, Toff  Whiteboard 
Mar 17  Operations on density operators. Theorem: Physically indistinsuishable iff same density operator. Toy crypto protocol is secure. Quantum onetime pad.  Density, DensityU, DensityM, DensityX, DensityPhysInd, QOTP  Video, Whiteboard 
Mar 23  Unitaries and measurements on density ops. Observables.  Density, DensityU  Whiteboard 
Mar 24  Partial trace. Quantum operations.  ParTr, QOper, QOperAlt  Video, Whiteboard 
Mar 30  Tracing out buffer qubits in $U_f$. Trace as a quantum op. Replace operation.  ParTr, QOper  Whiteboard 
Mar 31  Statistical distance. Trace distance. Short mentions not in notes: Fidelity. Optimal distinguisher  SD, SDSumDef, SDProps, TD, TDMaxDef, TDSD, TDProps  Video, Whiteboard 
Apr 06  Trace distance of biased distributions. QOTP without 0keys. TD between any two states.  SD, SDSumDef, TD, TDProps  Whiteboard 
Apr 07  Quantum key distribution: Intro. Security definition. Protocol overview. First step (distributing Bell pairs).  QKDIntro, QKDSecDef, QKDProto, Bell, TildeNotation  Video, Whiteboard 
Apr 13  Prob. of measuring key after QKD. Alternate sec def of QKD. SMT from QKD.  QKDSecDef  Whiteboard 
Apr 14  Quantum key distribution: Bell test. Measuring the raw key.  BellTest, BellTestAna, RawKey, RawKeyKeyDiff, RawKeyGuess, MinEnt, RawKeyEnt, RawKeyAna  Video, Whiteboard 
Apr 20  Alternate sec def for QKD (continued). Measuring key with t errors.  QKDSecDef, RawKeyGuess  Whiteboard 
Apr 21  Error correcting codes. Error correction step in QKD. Strong randomness extractors. Universal hash functions. Privacy amplification in QKD. Finished QKD security proof.  ECC, QKDCorr, Chain, QKDCorrAna, PrivAmp, RandExtQ, UHF, LHL, PrivAmpAna, QKDWrapup  Video, Whiteboard 
Apr 27  Last bit of key deleted or set 0. Error correction after randomness extraction. Extracting too much from a key. Problems with deterministic randomness extractors.  ECC, RandExtC, UHF  Whiteboard 
Apr 28  Shor's algorithm. Period finding. Factoring. Discrete logarithm.  Fact, Period, FactFromPeriod, DFT, DFTAlgo, Shor, DlogAlgo  Video, Whiteboard 
May 04  Implementing the Quantum Fourier Transform. The von Neumann extractor.  DFTAlgo  Whiteboard 
May 05  LWE problem (computational and decisional). Regev's cryptosystem. INDCPA security of Regev's cryptosystem.  BinCompLWE, CompLWE, DecLWE, Regev, RegevCPA  Video, Whiteboard 
May 11  Example of Regev's cryptosystem. The Short Integer Solutions problem. CollisionResistant hash functions from SIS.  Regev  Whiteboard 
May 12  Classical/quantum zero knowledge. Difficulty with rewinding in the quantum case.  ProofSys, ZK, GIZK, QZK, QZKProblem  Video, Whiteboard 
May 18  Aborting simulators  classical and quantum.  ProofSys, ZK, GIZK, QZK  Whiteboard 
May 19  Quantum rewinding. Constructing a quantum ZK simulator.  QRewind, QZKAna  Video, Whiteboard 
May 26  Schrödinger equation. Particle in an infinite potential well.  Physical  Video, Whiteboard 
Out  Due  Homework  Solution 

20210221  20210301  Homework 1  Solution 1 
20210301  20210308  Homework 2  Solution 2 
20210308  20210316  Homework 3  Solution 3 
20210315  20210323  Homework 4  Solution 4 
20210322  20210330  Homework 5  Solution 5 
20210329  20210406  Homework 6  Solution 6 
20210405  20210413  Homework 7  Solution 7 
20210412  20210420  Homework 8  Solution 8 
20210420  20210427  Homework 9  Solution 9 
20210426  20210504  Homework 10  Solution 10 
20210503  20210511  Homework 11  Solution 11 
20210510  20210518  Homework 12  Solution 12 
20210518  20210525  Homework 13  Solution 13 
In quantum cryptography we use quantum
mechanical effects to construct secure protocols. The paradoxical
nature of quantum mechanics allows for constructions that solve
problems known to be impossible without quantum mechanics. This lecture
gives an introduction into this fascinating area.
Possible topics include:
You need no prior knowledge of quantum mechanics. You should have heard some introductory lecture on cryptography. You should enjoy math and have a sound understanding of linear algebra.
[NC00] Nielsen, Chuang. "Quantum Computation and Quantum Information" Cambridge University Press, 2000. A standard textbook on quantum information and quantum computing. Also contains some quantum cryptography.
Further
reading may be suggested during the
course. See the "further reading" paragraphs in the lecture notes.