# Superposition and entanglement

## Superposition

One of the properties that sets a qubit apart from a classical bit is that it can be in superposition. Superposition is one of the fundamental principles of quantum mechanics. In classical physics, a wave describing a musical tone can be seen as several waves with different frequencies that are added together, superposed. Similarly, a quantum state in superposition can be seen as a linear combination of other distinct quantum states. This quantum state in superposition forms a new valid quantum state.

A typical example visualizing superposition is the double-slit experiment. This experiment is explained in the following video:

Qubits can be in a superposition of both the basis states $\left\lvert 0 \right\rangle$ and $\left\lvert 1 \right\rangle$. When a qubit is measured (to be more precise: only observables can be measured), the qubit will collapse to one of its eigenstates and the measured value will reflect that state. For example, when a qubit is in a superposition state of equal weights, a measurement will make it collapse to one of its two basis states $\left\lvert 0 \right\rangle$ and $\left\lvert 1 \right\rangle$ with an equal probability of 50%. $\left\lvert 0 \right\rangle$ is the state that when measured, and therefore collapsed, will always give the result 0. Similarly, $\left\lvert 1 \right\rangle$ will always convert to 1.

Quantum superposition is fundamentally different from superposing classical waves. A quantum computer consisting of $n$ qubits can exist in a superposition of $2^n$ states: from $\left\lvert 000... 0 \right\rangle$ to $\left\lvert 111... 1 \right\rangle$. In contrast, playing $n$ musical sounds with all different frequencies, can only give a superposition of $n$ frequencies. Adding classical waves scales linear, where the superposition of quantum states is exponential.

## Entanglement

One of the other counter-intuitive phenomena in quantum physics is entanglement. A pair or group of particles is entangled when the quantum state of each particle cannot be described independently of the quantum state of the other particle(s). The quantum state of the system as a whole can be described; it is in a definite state, although the parts of the system are not.