QUANTUM ENTANGLEMENT

By Suvir Rathore

Spin in the quantum world is the intrinsic angular momentum for an elementary particle, composite particle and atom nuclei. Fermions are particles with non-integer spin including leptons and quarks, the unit of which is the reduced Planck constant (h/2π), and bosons are particles with integer spin including the force carriers. What this means is that the motion of the particle in a magnetic field will be respective to its spin, whether it is, for example, spin 1 and spin 2 which are opposite.

As per the Pauli Exclusion Principle, two fermions cannot exist in the same quantum state (for the two wave functions would equal 0 if they could) which means you don’t fall through the floor. However bosons do not obey the Pauli Exclusion Principle and can therefore exist in the same quantum state, which makes it possible for technology such as lasers to function.

To create an entangled pair of particles, one can use a (non-linear) barium borate crystal, allowing light rays to interact in the non-inert substrate. Then through a process known as spontaneous (parametric) down conversion, forming two (lower energy) photons from 1, although there is a very low probability of this happening.

In a scenario where an entangled pair of photons are released from an electron and positron (anti-electron) annihilation collision, by the conservation of momentum the spin of photon A and photon B will sum to 0 meaning they are opposite, for the spin of the electron and positron had also summed to 0. However both photons are in a superposition of both (for example) spin up and spin down, which is true when the photons remained unobserved (interactions of any sort).

If the spin of photon A is measured, it has to be ‘observed’ and therefore its wave function will collapse. If the spin measured is up, then the wave function of photon B instantaneously collapses to reveal spin down, irrespective to distance. This means that theoretically, even if the entangled pair are located across the universe, their wave functions will collapse simultaneously when one is observed to reveal opposite spin. Of course this does not seem right, as it could mean that information travels faster than the speed of light, Einstein called this a ‘spooky action at a distance’ however it is not as simple as that.

One proposed solution was hidden variable theorem. Einstein, Podolsky and Rosen all strongly supported this (forming what was known as the great EPR paradox). It suggested that quantum theory in itself was incomplete, and that the two photons were destined to be either spin up or spin down, so that information did not seem to travel faster than the speed of light. The analogy used was this; Assume two boxes represent the two photons. In one box you put a right-handed glove and in the other box a left-handed glove. If you mix them up and send them a great distance and open one to find a right-handed glove, the other box would immediately reveal a left-handed glove. Bohr on the other hand suggested that this was wrong, and that both boxes originally had a right-handed glove and a left-handed glove, and the probability would be 50% of a box containing either.

It was not until Bell’s inequalities were satisfied to prove ‘EPR’ wrong thus showing how there were no hidden variables. That is not to say, however, that information travels faster than the speed of light, for the superposition of the photons being in either spin mean that there is a 50% chance of each it being either spin which cannot be influenced or determined, hence revealing that is it only a probabilistic event.

Entanglement can be used for ‘unhackable’ quantum networks. When encrypted information is transmitted, only these particles can access it in the entangled state. Therefore by measuring it, you are altering the state of them, hence the location at which it is intercepted can immediately be found out; Chinese scientists were able to achieve this over a distance of 1200km!