Lecture 6 Notes: Deutsch-Jozsa Algorithm
6.1 Tensor product of Hilbert spaces
Until now we have been concerned with the description and evolution of a single TLS. Although we
have examples of how it describes some real physical systems, of course many sys

Lecture 6 Notes: Tensor Product of Hilbert Space
6.1 Tensor product of Hilbert spaces
Until now we have been concerned with the description and evolution of a single TLS. Although we
have examples of how it describes some real physical systems, of course

Lecture 3 Notes: State Space
3.1 Introduction
Every physical theory is formulated in terms of mathematical objects. It is thus necessary to establish
rules to map physical concepts and objects into mathematical objects that we use to 5represent them
this

Lecture 2 Notes:
Mathematical Hilbert Space
Quantum mechanics is a linear theory, and so it is natural that vector spaces play an important role in it. A physical
state is represented mathematically by a vector in a Hilbert space (that is, vector spaces o

Lecture 4 Notes: Angular Momentum
4.1 Generalities
We have already seen some examples of systems described by two possible states. A neutron in an inte
taking either the upper or lower path. A photon linearly polarized either horizontally or vertically. A

Lecture 5 Notes: AC Stark Shift
In a previous lecture we characterized the time evolution of closed quantum systems asunitary, |(t) = U (t, 0) |
(0) and the state evolution as given by Schrodinger equation:
ii
d|)
= H|)
Equivalently, we can nd a dierentia

Lecture 7 Notes: Entanglement Measurement
7.1 Mixed States
Until now we have considered systems whose state was unequivocally described by a state vector.
Altho result of an observable measurement on the state is probabilistic, until now the state of the

Lecture 9 Notes: Uncertainty Relationships
9.1 Harmonic Oscillator
We have considered up to this moment only systems with a nite number of energy levels; we are now going to
consider a system with an innite number of energy levels: the quantum harmonic os

Lecture 10 Notes: Coherent States
We will now provide a quanto-mechanical description of the electro-magnetic eld. Our main interest will be in
analyzing phenomena linked to atomic physics and quantum optics, in which atoms interacts with radiation. Some

Lecture 8 Notes: The Kraus Representation Theorem
We now proceed to the next step of our program of understanding the behavior of one part of a bipar
system. We have seen that a pure state of the bipartite system may behave like a mixed state when
subsyst

Lecture 1 Notes: Introduction and Basics of Quantum Mechanics
1.1 Why study Quantum Mechanics?
Quantum mechanics (QM) is a fundamental and general theory that applies on a very
wide range of subatomic systems to astrophysical objects.
It is nowadays also