CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 15: Separable mappings and the LOCC paradigm
In the previous lecture we discussed separable operators. The focus of this lecture will be on
analogous concepts for mappings between operator s

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 14: Separable operators
For the next several lectures we will be discussing various aspects and properties of entanglement.
Mathematically speaking, we dene entanglement in terms of what it

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 13: Majorization for real vectors and
Hermitian operators
This lecture discusses the notion of majorization and some of its connections to quantum information. The main application of majori

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 12: Holevos theorem and Nayaks bound
In this lecture we will prove Holevos theorem. This is a famous theorem in quantum information
theory, which is often informally summarized by a statemen

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 11: Strong subadditivity of von Neumann entropy
In this lecture we will prove a fundamental fact about the von Neumann entropy, known as strong
subadditivity. Let us begin with a precise sta

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 10: Continuity of von Neumann entropy;
quantum relative entropy
In the previous lecture we dened the Shannon and von Neumann entropy functions, and established the fundamental connection bet

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 9: Entropy and compression
For the next several lectures we will be discussing the von Neumann entropy and various concepts relating to it. This lecture is intended to introduce the notion o

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 8: Semidenite programs for delity
and optimal measurements
This lecture is devoted to two examples of semidenite programs: one is for the delity between
two positive semidenite operators, an

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 7: Semidenite programming
This lecture is on semidenite programming, which is a powerful technique from both an analytic
and computational point of view. It is not a technique that is specic

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 6: Further remarks on measurements and channels
In this lecture we will discuss a few loosely connected topics relating to measurements and
channels. These discussions will serve to illustra

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 5: Naimarks theorem; characterizations of channels
5.1 Naimarks Theorem
The following theorem expresses a fundamental relationship between ordinary measurements
and projective measurements.

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 4: Purications and delity
Throughout this lecture we will be discussing pairs of registers of the form (X, Y ), and the
relationships among the states of X, Y, and (X, Y ).
The situation gen

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 3: States, measurements, and channels
We begin our discussion of quantum information in this lecture, starting with an overview of
three mathematical objects that provide a basic foundation

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 2: Mathematical preliminaries (part 2)
This lecture represents the second half of the discussion that we started in the previous lecture
concerning basic mathematical concepts and tools used

CS 766/QIC 820 Theory of Quantum Information (Fall 2011)
Lecture 1: Mathematical preliminaries (part 1)
Welcome to CS 766/QIC 820 Theory of Quantum Information. The goal of this lecture, as well as
the next, is to present a brief overview of some of the b