1. Bits and Bobs: The Quantum Theory of Information
Imperial College London
Bits and Bobs: The Quantum Theory of Information
Martin Plenio
Department of Physics and
Institute for Mathematical Sciences
Imperial College London

2. Information
Storage
Transmission
Processing

3. Information is Physical
Storage
Transmission
Processing
Physical Processes
Information is Physical

4. Classical Theory of Information (Shannon ~1948)
Information written as sequences of ‘0’ and ‘1’
Quantify information content by amount of space needed to represent message
20 KiloByte
150 KiloByte

5. Classical Theory of Information (Shannon ~1948)
Correlations
Two messages A and B are correlated if I can gain information about B by looking at A.
Michael
Martin
473
243
945
473
243
945 … …
What is this good for?

6. Classical Theory of Information (Shannon ~1948)
Correlations and Communication
Secret Correlations allow us to send secret information publicly
Number
Code
Public Message
(De)Code
Number
573 +
125 =
698 -
125 =
573
Reusing the same code loses secrecy
Secret correlations are used up in the process.

7. Constraints and Resources
Constraint: Restricts set of possible operations.
Resource: Allows to overcome restrictions due to constraint.
Resource cannot be increased under the constraint.
Secret communication over a distance:
Goal: Exchange secret messages over distance.
Constraint: Can only use public communication channels.
Resource: Secret correlations.
Are used up in the process

8. Classical Correlations
Alice
Bob

9. Experiments prove (Test of Bell inequalities):
Quantum Correlations
Alice
Bob
Experiments prove (Test of Bell inequalities):
Quantum correlation are different (stronger) than classical correlations and their generation requires the transfer of quantum particles!

10. Quantum Theory of Information
Physics is different for very small systems
Light
Wave
Atom
Particle

11. An experiment with Light/Electrons/Atoms...
© Reinhard Werner

12. An experiment with Light/Electrons/Atoms...
© Reinhard Werner

13. Quantum Theory of Information
Physics is different for very small systems
Light
Wave
Particle
but also
Atom
Particle
Wave
Superposition principle
Quantum Correlations

14. Quantum Theory of Information
Classical Bit
Quantum Bit
0 or 1
Classical register
Quantum register
101
N quantum particles systems require
2 numbers for their description
N classical systems
require N digits N

15. Classical Space is small …
Quantum space is big …

16. Going to a bigger space can help
Big is beautiful
Going to a bigger space can help
Real Analysis
Complex analysis

17. Quantum Information Processors explore all quantum space
Classical Space is small …
Quantum space is big …

18. Quantum Information Processors explore all quantum space
Possible Applications:
Quantum Cryptography
Quantum Computation
Universal Quantum Simulator for Quantum Systems
Enhanced Measurement Precision by Quantum Correlations
Quantum Secret Sharing
Quantum Fingerprinting …
In our quest to implement some of this we will learn to
control matter at the level of individual quanta.

19. A few possible Quantum Information Processors
Cavity QED
© ENS Paris
NMR
© CQC Oxford
Superconductors
© Quantum Transport Group
Delft University of Technology
Quantum dots
Trapped Ions
© University of Innsbruck
© T.Fujisawa, NTT Basic Research
In our quest to implement some of this we will learn to
control matter at the level of individual quanta and this must be useful for future technologies.