ECE 788 – An Introduction to Quantum Communication Theory
Description
This
course provides a basic introduction to quantum information theory (QIT) to
engineering students with a good background in linear algebra and
probability. QIT investigates the limitation of information processing and
communication as implemented on quantum-mechanical systems (i.e., system
operating at the atomic scale). The theory reveals the new possibilities
offered for communication and computing by the unique features of
quantum-mechanical systems, such as entanglement. For instance,
quantum-mechanical computers enable the efficient solution of problems, such
as prime factorization, that are assumed to be unsolvable with classical
computers. The need to understand information processing at the
quantum-mechanical scale also arises from the exponential trend towards
smaller and smaller systems that has thus far underpinned Moore’s law.
The course will start with an introduction to the basic postulates of quantum mechanics, covering the concepts of qubits, measurements, density matrices, entanglement and purification. The basic quantum communication protocols of entanglement distribution, quantum super-dense coding and quantum teleportation are introduced. Classical and quantum information measures are discussed with emphasis on the von Neumann entropy, the accessible information, the Holevo information and their properties. The von Neumann entropy is then interpreted in the light of Schumacher compression after having introduced the concepts of classical and quantum typicality. Examples of experimental systems implementing quantum communication will be provided.
Prerequisites
Basic knowledge of linear algebra and probability.
Instructor
Dr. Osvaldo Simeone
Email: osvaldo.simeone@ njit.edu
Phone: (973) 596-5710
Office: ECE 211
Textbook
B. Schumacher and M. Westmoreland, Quantum Processes, Systems, & Information, Cambridge, 2010.
Additional reading:
Mark M.Wilde, Quantum Shannon Theory, available on-line at http://arxiv.org/abs/1106.1445.
Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.
Emmanuel Desurvire, Classical and Quantum Information Theory: An Introduction for the Telecom Scientist, Cambridge University Press, 2009.
Requirements
There will a midterm (40%), a final exam (40%) and weekly assignments (20%).
General Readings
An excellent (gentle) introduction to aspects that will not be covered in this course, such as quantum field theory: Brian Cox and Jeff Forshaw, The Quantum Universe (And Why Anything That Can Happen, Does), Da Capo Press, 2012.
On the (mis-)interpretation of quantum mechanics: D. Kaiser, How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival, W. W. Norton & Company (June 27, 2011).
Lecture 1
V. Vedral, "Living in quantum world", Scientific American, 2011.
Lecture 5
Quantum theory from information theoretic principles: Chiribella et al
Lecture 6
On the Nobel prize and quantum information
Lecture 10
Exams
Tentative schedule
|
Date |
Plan |
Chapter covered |
|
Sept. 5 |
Introduction and brief history
The two-slit experiment Indeterminism, superposition and interference
|
1-2 |
|
Sept. 12 |
The qubit
Photon in the interferometer
Spin-1/2 particles, Bloch sphere Uncertainty |
2 |
|
Sept. 19 |
Hilbert space
Operators |
3 |
|
Sept. 26 - Oct. 3 |
Normal Operators
Basic measurements and projective measurements
Observables
Complementary and compatible observables
Uncertainty principle |
3 |
|
Oct. 10 |
Quantum information: Limits and distinguishability
Quantum key distribution: BB84 |
4 |
|
Oct. 17 |
Midterm |
|
|
Oct. 24 -Oct. 31 |
Composite quantum systems
Tensor product Hilbert spaces
Entanglement
Measurement of composite quantum systems |
6 |
|
Nov. 7 - Nov. 14 |
Partial measurements
Bell's theorem
No cloning theorem
Ebits
Superdense coding and teleportation
|
6-7 |
|
Nov. 28 |
Density operators
Mixed states as subsystems of an entangled system
Purification
Partial trace
Schmidt decomposition |
8 |
|
Dec. 5 |
Quantum computing
Universal gates
Deutsch-Jozsa algorithm |
18 |
|
Dec. 12 |
Guest lecture on the implementation of quantum computers |
|