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Protocols enabling protection and security of Information

Final Activity Report Summary - PEPSI (Protocols enabling protection and security of Information)

In the past decade quantum physics has entered computer science's world in quite an extraordinary way: quantum computers could in principle solve certain problems, such as integer factorisation and database search, much faster than standard computers (the intuition behind this speed-up is that quantum computers can efficiently perform many computations 'at once'). Furthermore, quantum communication protocols can transmit information with a degree of security much higher than standard cryptography protocols: the extra level of security is warranted by the validity of the physical laws themselves (intuitively, if an eavesdropper intercepts a quantum message, then quantum physics states that the act of reading its content will alter the message in a way that is detectable by the communicating partners, and that prevents the eavesdropper to decipher the original message).

The most important achievement of this project has been to extend considerably an abstract formalism for describing and reasoning about quantum computation. Abstraction makes things easier to understand and to use: just think how easier it is nowadays to use personal computers with graphical user interfaces compared with the command-line interfaces of twenty years ago! However, it is widespread practice to treat quantum computation at an unnecessarily low level of abstraction, using for example circuit diagrams. Our formalism enables us instead to treat quantum algorithms as proper programs, raising the level of abstraction and thereby freeing us from thinking about implementation details: these are the well-established benefits of high-level programming languages.

In particular, we have shown how to extend the approach of formal methods to include quantum computation. Using our formalism we can give a high-level description (a specification) of an algorithm and then derive its quantum implementation via a series of design 'refinements': we have exemplified that concept by providing a derivation of Grover's important quantum search algorithm. Also, we have addressed the important issue of faulty hardware: what happens to a quantum program when a component of the quantum computer is faulty?

We have provided a simple model for faulty quantum measurements (one of the two 'building blocks' of quantum computation) and showed how to use it by modelling a faulty version of the eavesdropping mechanism of a quantum protocol and deriving efficiency bounds for that device - 83 % in our example.