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 (not including title page and bibliography). Your paper

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/Eigenvalue Rule:
A state possesses the value of a property rep

PL 2124 - Philosophy of Quantum Mechanics
Summary of Interpretations of Quantum Mechanics
Interpretation
EE Rule
Dynamics
Problems
Literal
("Copenhagen")
yes
Schrdinger dynamics
Projection Postulate.
Measurement Problem
Local Hidden
Variables with VD*
n

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 obey the axioms for classical
probability theory?
2.
Wha

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?
2.
In your own words, explain why it is a matter of q

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 determine
whether or not a state in a superposition has

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, given the initial position of a black electron, we ca

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 ship-board pad,
his body completely disintegrates. Down on Pl

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. What property
does the projection operator P|a
25
2.
repre

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 non-local, or
that QM is incomplete.
2.
If the state of a system

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 non-orthogonal states of quantum systems, what is the random
element associated with Alice's encoding procedure?

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 argue that quantum information is not essentially diff

PL 2294 - Quantum Mechanics and Information
Assignment #3: 2-Particle States and the Eigenvector-Eigenvalue Rule. Due Tues 2/24
1.
Suppose a 2-particle system is in an entangled state represented by
|Q = |51|72 + |91|112,
where |x1 and |y2 are eigenstates

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
0
|black =
1
|white =
"
-"
(a) Show that |hard and |sof

PL-UY 2294 Quantum Mechanics and Information
Assignment #1. Due: Tues 2/10.
1.
The 2-path experiment involves electrons with the properties of Hardness and Color and the Big Question we
asked was: "What path does an individual white electron take?" The an

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 of two linear subspaces is not in general the same as t

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 it in the slightest way. Here's an
example: Suppose yo

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 Individuals
1. Property-Based "Bundle" View
An individual = a

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
(non-Boolean) logic.
Consequence: QM probabilities do not satisfy the

13. Decoherence and Consistent Histories
I. Quantum Probabilities and Interference
Topics:
I. Quantum Probabilities and Interference
II. Decoherence
III. Consistent Histories
Basic Idea: Classical probability theory is based on classical (Boolean) logic.

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. States: The state of a physical system is given by both a w

14. Quantum Particles: Identity and Individuality
I. Approaches to the Notion of Individuality
1. Property-Based "Bundle" View
An individual = a bundle of properties.
So: Properties individuate objects. No two individuals can be completely
indiscernible

12a. Modal Interpretations
Let's return to using Hilbert spaces to represent QM state spaces, and
operators to represent properties.
Recall: The Kochen-Specker Theorem says that the properties associated with
a Hilbert space H can't all have values at t

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 send 2 classical bits using just one qubit?
Answer: Use

10. The Dynamics by Itself
Consider composite system of human observer h, Color measuring device m,
and electron e.
Suppose: Pre-measurement state is |readyh|readym|harde.
Then: Schrdinger dynamics entails post-measurement state will be:
1
2
|believes

07. Quantum Information Theory (QIT), Part I.
I. Qubits.
1. C-bits vs. Qubits
Classical Information Theory
C-bit = a state of a classical 2-state system: either "0" or "1".
Physical examples:
The state of a mechanical on/off switch.
The state of an ele

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 measurement, states change via the Projection Postulate:
When a

08a. The Kochen-Specker Theorem
How Should Superpositions be Interpreted? Part 2
(A) Literally (QM description is complete):
Options:
EPR say: non-local!
(1) Standard Claim: The properties of a quantum system in a
superposed state are indeterminate (do n

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. Qubits
Classical Information Theory: Based on concept

01. The 2-Slit 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 space
lump of matter
model - Newtonian gravity
Extends to