# Entanglement¶

**Composite systems** i.e. quantum systems that are made of several particles,
can also be in a superposition of states, like single particles do.

The strange fact is that we can achieve states were the several particles are **strongly correlated**:

We know that in this case if particle

ais measured in state \(\ket{a_1}\), then particlebwill always be measured in \(\ket{b_1}\). This entangled state would be described by this formula

The result of the measurement of *a* cannot be known *a priori*,
but the result of the measurement of *b* will be certain.
This property is called **entanglement**,
and occurs when the wave function cannot be written as a product state in terms of the states
of the individual particles.

The concept of **measurement** in quantum mechanics can be interpreted as a **collapse** of the state
(*Copenhagen interpretation*): one of the terms in the superposition will be randomly “choosen”.
This leads to a paradox in the sense that for separated entangled particles,
this “choice” will be done at the same time at arbitrary far locations!
Einstein called this the “spooky action at a distance”.

How the correlation occurs in more complex settings cannot be explained by classical physics and statistics. A thorough and definitive experimental proof of the validity of the rules of quantum mechanics wrt. entanglement was achieved with the so-called EPR Experiments based on the Bell Inequalities.

A few examples of realization of entanglement are listed in the physical implementation section: This is real!