Quantum entanglement surpasses even a magician’s tricks

Quantum entanglement is a phenomenon that has no equivalent in everyday physics. Of all the phenomena of quantum physics, it is one of the oddest. In this science blog post, professor Teiko Heinosaari describes how a magician with dice could make his trick more impressive using quantum entanglement.

Noppa Teiko Heinosaaren kädessä
Published
9.4.2025

Teksti: Teiko Heinosaari | Kuvat: Petteri Kivimäki

Quantum entanglement cannot really be illustrated in any other way than by comparing it to magic. Thus, our current story begins with a magician who has two magic dice. He shows them to two friends, Antti and Bertta. When one of the dice is rolled, you notice nothing extraordinary, as the dice gives all face value at random. But when the two dice are rolled at the same time, things become more peculiar – every time, the dice give the same face value. 

Antti and Bertta went to separate rooms to roll the dice, recorded the face values, and came then back to compare the results. Indeed, they had got identical results each time.

At first, Antti and Bertta were astonished by the dice, but after giving it some thought, they did not find the dice so odd after all. Perhaps the magician had drawn up a long list of numbers beforehand and then constructed some kind of mechanism inside the dice, which made the dice give the pre-defined face values. It doesn’t require any magic after all.

Can you fool a magician?

Antti continued pondering what kind of a trick could indicate the involvement of magic. This would require behaviour from the dice that cannot be accomplished through any pre-drawn list of numbers and built-in mechanism.

Antti came up with the following trick, which requires four dice. Antti has a blue and a green dice, while Bertta has a red and an orange dice. They go to separate rooms to roll their dice. The dice are rolled for several rounds and at the beginning of each round both Antti and Bertta choose either of their dice at random. The choice is kept secret until the dice have been rolled.

If the rolled pairs of dice in turn are blue–red, blue–orange, or green–red, the sum of the face value must be an even number. Then again, if the combination is green–orange, the sum must be an odd number.

The magician tried to make dice of this kind. It is not immediately obvious that it would be impossible to get the required face values by means of a number list and an in-built mechanism in the dice. 

Antti had thought the challenge through, however.

Let’s say you make a table consisting of 16 choices, where the face value of each of the four dice is either 1 or 2. From the table, you can see that every possible choice is somehow in contradiction with the above requirements. This is alsotrue when the face values are something other than 1 or 2. Hence, if the dice are rolled for a longer time and then we review what happened in the trick, it can be seen that in a fourth of the instances the dice give inadequate face values. Thus, using a pre-drafted list, the trick could succeed in 75 out of 100 attempts.

The dice trick would benefit from quantum entanglement

The magician gave up as he was unable to make the dice that Antti had requested. Bertta started to think of a way by which the magician, who might not have studied quantum physics, could be fooled in turn. Bertta told the magician they could conjure up the desired magic dice.

Antti and Bertta went to their rooms and took along some quantum systems prepared beforehand. The magician could say whether Antti reports the face value for the blue or the green dice and Bertta for the red or the orange dice. Instead of rolling the dice, Antti and Bertta conducted measurements on their quantum systems and reported the results. 

When the quantum systems are in suitable states and the measurements are conducted appropriately, Antti and Bertta can succeed in the trick even 85 times out of 100.

The essential point here is that the quantum systems are prepared for a jointly entangled state. 

The magician was astonished: How on earth could Antti and Bertta exceed the results achieved by the pre-defined number list! Of course, he would have been even more astonished about a perfect result, but there is a limit to everything, as we know.

Quantum entanglement is not about a gravitation-like interaction

So what is quantum entanglement all about? Quantum entanglement is a shared quality of two or more quantum physical systems which may emerge when they have been in mutual interaction. In an entangled state, the objects remain as if one even when separated.

It is important to understand that entanglement is not interaction in the same sense as gravitational interaction, for example. Entanglement shows so that system qualities can be correlated more strongly than would be possible in everyday settings. This is the very feature that Antti and Bertta utilised in their trick.

Quantum entanglement has its limits, however, and the correlation is not as strong as would be mathematically possible. On the other hand, it makes quantum entanglement such an interesting phenomenon.

In terms of quantum technology, the use of entanglement is not straightforward nor is it an all-enabling magic gimmick. We have nevertheless learnt to make use of quantum entanglement in data transfer and computing in a way that is impossible without quantum physics. In the future, people will certainly find further applications for it. Although quantum entanglement seems highly extraordinary, it is today an essential part of quantum technology.

Real life is sometimes stranger than magic.