PLUY 2294 Quantum Mechanics and Information
Assignment #1. Due: Tues 2/10.
1.
The 2path experiment involves electrons with the properties of Hardness and Color and the Big Question we
asked was: "Wh
07. Quantum Information Theory
These notes generally follow the
presentation in Rieffel & Polak (2000)
Topics:
I. Qubits
II. Quantum Cryptography
III. Quantum Teleportation
IV . Quantum Computation
I.
PL 2294  Quantum Mechanics and Information
Paper Assignment. Due Tuesday May 5.
(a) Choose one of the following topics and respond to it in an essay of no less than 5 pages and no more than 7
pages (
PL2124  Philosophy of Quantum Mechanics
5 Principles of Quantum Mechanics
(A) States are represented by vectors of length 1.
(B) Properties are represented by Hermitian operators.
Eigenvector/Eigenva
PL 2294  Quantum Mechanics and Information
Assignment #12: Decoherence and Consistent Histories. Due Tuesday 5/5.
1.
How are probabilities defined by the Born Rule different from probabilities that o
PL 2294  Quantum Mechanics and Information
Assignment #11: Modal Interpretations and Quantum Logic. Due Tuesday 4/28.
1.
What is the Problem of Imperfect Measurements for the KHD Modal Interpretation
PL 2294  Quantum Mechanics and Information
Assignment #8: Collapse and GRW. Due Tues 4/7.
1.
Explain in your own words why it is possible in principle, but impossible in practice, to experimentally d
PL 2294  Quantum Mechanics and Information
Assignment #10: Bohm's Theory and Modal Interpretations. Due Tuesday 4/21.
1.
Explain the sense in which Bohm's Theory is deterministic.
2.
In Bohm's Theory
PL 2294  Quantum Mechanics and Information
Assignment #9: Many Worlds, Many Minds. Due 4/14.
1.
Suppose the transporter in (the original) Star Trek malfunctions: When Capt. Kirk steps onto the shipb
PL 2294  Quantum Mechanics and Information
Assignment #7: KS and Measurement. Due Tuesday 3/31.
1.
Suppose A is an operator that represents a property and that has eigenvectors a1, a2, . , aN. Wha
PL2294  Quantum Mechanics and Information
Assignment #4: EPR & Bell. Due Tuesday 3/3.
1.
Explain, in your own words, why a literal interpretation of superpositions entails that either QM is nonlocal
PL 2294  Quantum Mechanics and Information
Assignment #6: QIT Part 2. Due Tuesday 3/24.
1.
In the protocol for distribuing a secret key using nonorthogonal states of quantum systems, what is the ran
PL 2294  Quantum Mechanics and Information
Assignment #5. QIT. Part 1. Due Tuesday 3/10.
1.
In your own words, describe the essential differences between a qubit and a classical bit.
2.
How might you
PL 2294  Quantum Mechanics and Information
Assignment #3: 2Particle States and the EigenvectorEigenvalue Rule. Due Tues 2/24
1.
Suppose a 2particle system is in an entangled state represented by

PL 2294  Quantum Mechanics and Information
Assignment #2. The Principles of QM. Due: 2/17
1.
Suppose eigenvectors of Hardness and Color are given by the following column vectors:
hard =
1
soft =
0
PL 2294  Quantum Mechanics and Information
Extra Credit#2 (Optional). Due Tues 4/28.
1.
Explain two differences between quantum logic and classical logic.
2.
In your own words, explain why the union
PL 2294  Quantum Mechanics and Information
Extra Credit#1 (Optional): Interaction Free Measurements (IFM). Due Tuesday 3/24.
QM allows you to perform measurements on a system without interacting with
14. Quantum Particles: Identity and Individuality
I. Approaches to the Notion of Individuality
Topics:
I. Individuality
II. Fermions and Bosons
III. Classical and Quantum Statistics
IV. Quantum Indivi
13a. Quantum Probabilities and Interference
Classical probability theory is based on classical (Boolean) logic.
The probabilities defined by the Born Rule in QM are based on quantum
(nonBoolean) lo
13. Decoherence and Consistent Histories
I. Quantum Probabilities and Interference
Topics:
I. Quantum Probabilities and Interference
II. Decoherence
III. Consistent Histories
Basic Idea: Classical pro
11. Bohm's Theory (Bohmian Mechanics)
Motivation: Replace Hilbert state space of QM with one
that is more classical and reproduces QM predictions.
4 Principles of Bohmian Mechanics
David Bohm
1. Stat
14. Quantum Particles: Identity and Individuality
I. Approaches to the Notion of Individuality
1. PropertyBased "Bundle" View
An individual = a bundle of properties.
So: Properties individuate obje
12a. Modal Interpretations
Let's return to using Hilbert spaces to represent QM state spaces, and
operators to represent properties.
Recall: The KochenSpecker Theorem says that the properties assoc
07. QIT, Part II.
2. Quantum Dense Coding
Goal: To use one qubit to transmit two classical bits.
But: One qubit (supposedly) only contains one classical bit's worth of
information!
So: How can we s
10. The Dynamics by Itself
Consider composite system of human observer h, Color measuring device m,
and electron e.
Suppose: Premeasurement state is readyhreadymharde.
Then: Schrdinger dynamics
07. Quantum Information Theory (QIT), Part I.
I. Qubits.
1. Cbits vs. Qubits
Classical Information Theory
Cbit = a state of a classical 2state system: either "0" or "1".
Physical examples:
The st
09a. Collapse
Recall: There are two ways a quantum state can change:
1.
In absence of measurement, states change via Schrdinger dynamics:
(t1) ! (t2)
Schrdinger
evolution
2.
In presence of measurem
08a. The KochenSpecker Theorem
How Should Superpositions be Interpreted? Part 2
(A) Literally (QM description is complete):
Options:
EPR say: nonlocal!
(1) Standard Claim: The properties of a quant
01. The 2Slit Experiment
What is the world made of ?
The dominant view in the 17th & 18th centuries: Newtonian corpuscular
ontology:
stable corpuscles of
matter  held in
place by forces
empty spac