All posts by pawelkurzynski

Are we prisoners of reversibility?

(some loose thoughts that are definitely not new, but which I find quite fascinating)

A broken glass will not fix itself; you can either face the fury of your neighbors or forget your ball and run. Whatever you chose, your relationship with these people will change for ever. Some things are irreversible and we have to accept it.

Or do we?

All of us who work in quantum information surely remember the first lesson that quantum gates are unitary and that the evolution of a qubit can be viewed as a rotation of a vector. We also immediately find that these rotations are “nice” because they can be inverted. However a few lessons later we learn about Kraus operations and Master equations, and we find that in fact irreversibility is implicit. I don’t know about you, but my first impression was that quantum irreversibility is a very messy business. Of course, we can refer to “the Church of the Larger Hilbert space” and purify everything by extending the system and making everything unitary again, but in the end does larger mean simpler?

Correct me if I am wrong, but I think that many people believe that the power of quantum computation, not taking into account the measurement phenomena, is going to be based on unitarity. Perhaps they are right. Up until now all famous quantum protocols are based on unitary gates. Moreover, since the era of “information is physical” and the works of Landauer and his colleagues, wehave started to believe that the future of computation will rely on reversibility.

But is it good to fight with irreversibility? First of all, let us clarify that irreversibility does not necessarily mean mess, i.e. it does not imply randomness and unpredictability. The AND gate is fully deterministic – if you know the input, you know the output. The thing is that it is not the other way around. If you want to trace back your computation, at some point you will have to guess. This may not be a problem since time flows in one direction so why bother? (well, let’s leave this for the different post…) Everybody has to admit that the AND gate is a very elegant and simple piece of computational architecture. So irreversibility can be a source of simplicity and elegance.

Still, simplicity and elegance is not enough, so let’s not use Occam’s Razor yet. The fun starts when you realize that actually irreversibility is a very powerful phenomenon. This idea was introduced by Poincare and Boltzman, and was further developed by Prigogine and others. Reversibility is in a sense boring, since in a finite system you are closed in a loop. Reversibility leads to reoccurrencesand nothing new and stable can emerge, since you will always go back to the start. On the other hand, irreversibility demands that you have to forget the past – you will not necessarily come back to the start. Even better, something new can emerge.

Ideas like emergence, self organization and complexity have been around in science for some time. In particular, very simple computer science models, like cellular automata, can nevertheless exhibit these nontrivial phenomena. On the other hand, the unitary quantum version of cellular automaton does not seem to possess so many intriguing features. Therefore, the natural question is: why stick to unitarity?

There are “complex” quantum mechanical phenomena that do not work without irreversibility. Laser cannot work if the system follows only a unitary evolution and the dynamics of bosonic condensation does not seem to be unitary.  Therefore, can irreversibility bring something new to quantum information?