[[Quantum mechanics MOC]]
# Entangled state

Let $H_{A}$ and $H_{B}$ be [[Hilbert space|Hilbert spaces]].
A state $\ket{\psi}_{AB} \in H_{A} \otimes H_{B}$ is said to be **separable** if it is the tensor (outer) product of states of the constituent systems, i.e. $\ket{\psi}_{AB} = \ket{\psi}_{A}\otimes \ket{\psi}_{B}$.
A state is said to be **entangled** if it is not separable.

Entanglement appears to be the crucial factor in obtaining exponential speedups in [[Quantum computing MOC|quantum computing]] over classical computing.[^2011]

[^2011]: 2011\. [[Sources/@williamsExplorationsQuantumComputing2011|Explorations in Quantum Computing]], §1.4.4, p. 22

## See also

- [[Maximal entanglement]]

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