Monthly Archives: February 2013

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?

By Jove what is Reality?

Zhuangzi once said: ‎”Once upon a time, I, Chuang Chou, dreamt I was a butterfly, fluttering hither and thither, to all intents and purposes a butterfly. I was conscious only of my happiness as a butterfly, unaware that I was Chou. Soon I awaked, and there I was, veritably myself again. Now I do not know whether I was then a man dreaming I was a butterfly, or whether I am now a butterfly, dreaming I am a man. Between a man and a butterfly there is necessarily a distinction. The transition is called the transformation of material things.”

These musings are attributed to a Chinese philosopher who died circa 286 BC. They are also thoughts that many of us ask ourselves at some stage of our lives. We quickly dismiss these questions as irrelevant, too philosophical or simply unverifiable and get down to brass tacks. After all, it is impossible to know if I am dreaming now, or more fashionably, if I am a program in a computer simulation. Or is it really?

I don’t know an answer to this question but I recognise it as an important one. Hell, it is the question to ask! Don’t you agree?

However difficult this question may be, it has variants which are perfectly verifiable in a laboratory. Let me discuss one of them. The one I particularly like.

We all know that there are only two types of particles in this Universe: bosons and fermions. We also know that certain conditions an even number of fermions can behave like a boson. The simplest example is the hydrogen atom H (atomic hydrogen) whose bosonic behaviour was confirmed by Bose-Einstein condensation in 1998 after 20 years of hard experimental work (Phys. Rev. Lett. 81, 3811 (1998)).

The question arises: Is it possible that all bosons we observe in the Universe are made of fermions? Are we being fooled into believing that there are fundamental bosons? More fashionably: Is there a device independent test to reveal the veracity of this claim?

I’d like to stress here the words “device independent”. This means that the test should not assume anything about the physics of the investigated particles, i.e., it should give a definite answer independently of any known physical theory.

In our recent paper in New Journal of Physics titled “Particle addition and subtraction channels and the behaviour of composite particles” (NJP 14, 093047 (2012)) we discuss this question. Check it out!