Quantum Entanglement

Every object around us is made up of massive particles. Collectively, we refer to these particles as matter. However, there is a deeply similar entity in the universe that we do not encounter on a daily basis – antimatter. Antimatter is composed of antiparticles, which have the same mass as their particle counterparts but are oppositely charged. For example, the antiparticle of electron, called positron, is positively charged, while the electron is negatively charged. When a particle comes in contact with an antiparticle, both of them are destroyed while releasing an enormous amount of energy. This process is called annihilation.

Let us imagine a situation where a particle collides with its antiparticle, electron with a positron, for instance, while the electron has a spin opposite to the spin of the positron at the time of the collision, so that their overall spin is zero. Once they collide, annihilation occurs instantly. In this case, the annihilation energy is released in the form of two photons of gamma radiation. Let us label the photons as photon A and photon B.

As mentioned earlier, spin represents the intrinsic angular momentum. That is to say that spin obeys the law of conservation of angular momentum, which states that the total angular momentum of a system does not change over time. In other words, if the total spin of the system of the electron and the positron was zero, the total spin of the photons A, B has to be zero as well. Photon A therefore must have a spin that is opposite to the spin of photon B. For illustration, let us label the spins of the photons as spin 1, spin 2.

However, remember that unless a quantum object is observed, it is in a superposition of all possible states. Photon A is therefore in a superposition of spin 1 and spin 2. The same thing applies to photon B. The spin of neither of the photons is defined, but it is given that the spin of one photon must be opposite to the spin of the other photon.

If somebody observes one of the photons (say, photon A) and tries to measure its spin, its wave function collapses, and the photon obtains only one spin (say, spin 1). To fulfil the law of conservation of angular momentum, immediately after the wave function of photon A has collapsed, the wave function of photon B must collapse as well, so that the total spin of photons A and B stays zero.

In other words, the photons are in a state wherein an observation of photon A immediately influences the state of photon B, regardless of the distance between the photons. This state of a kind of superposition, where observation of one object determines the state of another object, is called quantum entanglement. Mathematically we can write the entangled state of photons A, B with spins 1, 2 as follows:

|𝛙⟩ = |𝟏_𝑨⟩|𝟐_𝑩⟩ + |𝟐_𝑨⟩|𝟏_𝑩⟩