Bits and Bobs: The Quantum Theory of Information

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Presentation transcript:

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 www.imperial.ac.uk/quantuminformation

Information Storage Transmission Processing

Information is Physical Storage Transmission Processing Physical Processes Information is Physical

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

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?

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.

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

Classical Correlations Alice Bob

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!

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

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

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

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

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

Classical Space is small … Quantum space is big …

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

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

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.

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.