**What does it mean for two things to be identical? **

Intuition tell us that if you are able to do a measurement or experiment such that you can detect a difference, then those two items are not identical. However, this statement of identical seems to be dependant on the abilities of the experimentalist. But what about if instead of considering some classical macroscopic objects whose distinguishability is dependant on the experimentalist, we instead consider fundamental particles, such as two electrons, existing in the quantum realm. As these particles are fundamentally the same the definition of identical is no longer dependant on the abilities of the experimenter to distinguish them but is a characteristic of the particles themselves.

This quantum nature of indistinguishable has an important consequence when considering systems of these identical particles. This consequence is called the symmetrisation principle, interested readers should resort to Feynman’s lecture notes (Vol III Ch 4.). A consequence of this symmetrisation is that the state of the full system now appears to have an important quantum property, known as entanglement. This is the quantum property once described by Einstein as “Spooky action at a distance” but is now expected to play an essential part in quantum computation and communication. However, we now have a problem, despite these identical particles being formally entangled how do we utilize it when we can’t tell which particle is which?

**The problem and solution is described in the following situation…**

Imagine you are presented with two individuals sitting close next to each other. They are dressed completely identically wearing the same clothes, of the same size and shape and seem to always copy each other’s movements. However, you know that in reality one of the individuals is in fact not real and is just a ventriloquists dummy being controlled by its identical counterpart!

Your task is to determine which one of the individuals is the ‘real’ human being and which is just made of wood. However, when you ask the pair the question, “which one of you is real?” The skilled ventriloquist while moving his mouth and saying the words “I am” makes the dummy’s mouth moves identically. From your position it is completely impossible to determine which one of the two individuals actually said the words, and is therefore the human, and which is the dummy just mouthing along.

**What’s the solution?**

Well, the problem is that with the characters standing next to each other, they cannot be addressed individually. However, if you separate the two characters such that the ventriloquist can no longer reach behind the dummy and mimic his own movements, you now have the upper hand. Most importantly you can now address the characters individually. This means that any question which you address to the dummy can no longer be faked by the ventriloquist and you can correctly determine who is who.

The same problem and solution applies to our systems of identical particles. Initially, because all the particles are all in the place, one can pretend to be the other, this is the symmetrisation principle. However, upon separating the particles the symmetrisation principle no longer applies and the particles can be individually addressed and the entanglement extracted.

In our recent work, we develop a consistent mathematical framework which fully describes the process of extracting entanglement from such systems of identical particles. A perfect example of such a system being a Bose-Einstein condensate, an incredibly cold ensemble of identical particles, know to show this interesting identical particle entanglement property. In collaboration with a group of experimentalists in Basel, Switzerland, we show that our mathematical framework consistently describes the process of extracting entanglement from a Bose-Einstein condensate and can even be used to lower bound the amount of entanglement they can experimentally extract and measure. In addition to revealing something fundamental about the nature of being identical in the quantum realm, it’s hoped that with this framework and the well-studied platform of Bose-Einstein condensates in place, the applicability and future implementation of this work *speaks for itself.* 😉

The example of identical particles in physics seems to require a notion of the cardinality of a set (number of particles) without any assumption that there exists a property that can be used to distinguish the elements of the set. Physics often isn’t interested in the technicalities of set theory. and the foundations of mathematics. I wonder if logicians have studied the implications of: Assume a set omega exists with the property it contains at least two elements and no equivalence relation (of any sort) can be defined on its elements where there are at least two elements that are not equal in that equivalence relation.

In classical physics,we might skirt the issue by saying that “identical’ is an equivalence relation defined with respect to a limited number of properties. There may exist other properties that distinguish “indistinguishable” particles. Is this way of thinking equivalent to imagining “hidden variables”?

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