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…