# Entanglement Entanglement is the state when multiple qubits have dependency between them. This means they can't be expressed as tensor multiplication of individual qubits. ## Examples - The first and second qubits in $\frac{1}{\sqrt 2}(|00\rangle+|10\rangle)$ are not entangled because $\frac{1}{\sqrt 2}(|00\rangle +|10\rangle) = \frac{1}{\sqrt 2}(|0\rangle + |1\rangle) \otimes|0\rangle$ - Bell state $\frac{1}{\sqrt{2}} \big(|00\rangle + |11\rangle\big)$: The first and second qubits are entangled. Proof: by way of contradiction , assume that their are not entangled i.e., there are $a,b,c,d$ s.t. $ \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)=(a|0\rangle+b|1\rangle)\otimes(c|0\rangle+d|1\rangle) =ac|00\rangle+ad|01\rangle+bc|10\rangle+bd|11\rangle $ $ac=bd=\frac{1}{\sqrt 2}$, $ad=bc=0$ which is a contradiction as the first equation require that $a,b,c,d\not=0$ but the second equation require that at least one fo $a,b,c,d$ is zero. Contradiction. Related: [[Quantum Teleportation]], [[Bell state]] Tag: #math, #tech ## Created 2026-02-06 11:44