## How quantum physicists amplify randomness

Once again quantum physics gives us philosophical implications: physicists showed how a small amount of randomness can be amplified without limit.

Classical physics is deterministic: for example, we can determine the position and velocity of a particle at any time in the future. Quantum theory, on the other hand, states that there exist processes which are fundamentally random: for instance, the outcomes of measurements of quantum particles seem to be determined entirely by chance. This is why Einstein argued in a publication in 1935 that the quantum theory is incomplete, and yet another kind of higher theory must exist, but up to the present time there has been no proof either that the world is purely deterministic and all randomness is due solely to a lack of knowledge about certain events, or that everything happens purely by chance. However, ETH Zurich physicists have now succeeded in showing in a thought experiment that randomness can be amplified. The results, published in the scientific journal Nature Physics, may also have practical applications.

#### Free choice is decisive for a representative outcome

Experiments in physics always depend on a large number of variables. To obtain a representative result, the choice of the variables – like the selection of the people questioned in an opinion survey – must be completely free and random. The entirely free – random – choice of variables is also important in information technology, for example, for efficient simulations. It is also extremely important for encoding messages, i.e. in cryptography, and for the random number generators in gambling casinos. If the latter work badly and a fraudster can see through them, he can exploit this to his advantage.

#### How random is a choice of variables?

In their study, the physicists Roger Colbeck, postdoctoral researcher, and Renato Renner, Professor at the Institute for Theoretical Physics of ETH Zurich, investigated which minimum conditions must be fulfilled in order for a selection of variables to count as absolutely free, and for this selection not to be already practically “pre-programmed” through earlier events. In this study the physicists defined that a variable counts as being chosen freely and at random if it is not correlated with other variables at this or an earlier moment in time.

In 1964 the physicist John Stuart Bell developed what is known as Bell’s inequality, which in simple terms states that there are measurements whose results are not pre-determined and are thus random. The experiments proposed by Bell to prove his theorem, which are based on measuring the entanglement of quantum-mechanical particles, did indeed show this, but only subject to the fundamental condition that the measurements performed during the experiment were chosen completely freely and at random. It is like arguing in a circle: the existence of randomness is again presupposed.

#### Making use of quantum mechanical laws

The scientists now made use of entanglement and locality – the fact that for example a local event on the Earth does not exert any direct influence on another planet – to show that beyond a certain point “weakly” indeterministic situations can be amplified to such an extent that they are completely random.

This is achievable for example with two entangled quantum particles that are strongly coupled but are then measured independently of one another. The scientists’ calculations showed that the quantum correlation between the bits can be so strong that they cannot be correlated with anything existing previously. This means that the results are completely random, whereas only weak randomness is needed for the choice of the measurement.

The two
scientists stress that they have not thereby proved that the world is
non-deterministic. However, they say there is nothing in between. The existence
of weak randomness automatically implies that there must be an unlimited amount
of strong randomness. However, Colbeck says it is first of all necessary to
achieve a particular “randomness threshold”: “Our method allows randomness to
be amplified once a certain threshold has been reached. It would now be
interesting to know whether this threshold can be made arbitrarily small by
using improved methods.” This would then mean that an arbitrarily small amount
of indetermisism would be sufficient to generate an unlimited amount of
randomness.

###### NCCR Quantum Science and Technology

The
study is another successful project carried out in the context of the NCCR-QSIT headed by ETH Zurich Professor
Klaus Ensslin.**The Wolfgang Pauli lecture on the topic:**

There was a lecture on this topic by Avi Wigdersonon 10.05.2012 as part of the Wolfgang Pauli lectures. In contrast
to the paper by Colbeck and Renner, however, Wigderson is concerned with the
“randomness” of a purely classical world. According to Renner, randomness
cannot be amplified in this world, and one must attempt to make do with “weak
randomness”.

###### Literature reference:

Colbeck R & Renner R: Free randomness can be amplified, Nature Physics (2012), Advance Online Publication, DOI: 10.1038/NPHYS2300

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