Entanglement

Entanglement is what Einstein famously called “spooky action at a distance.” It is a uniquely quantum phenomenon where two or more qubits become linked such that the state of one qubit cannot be described independently of the state of the others.

Start from $|00\rangle$. Apply H to qubit 0 to put it in superposition, then CNOT (control q0, target q1) to entangle the pair — the probabilities collapse to 50% $|00\rangle$ and 50% $|11\rangle$. Now measure repeatedly: the two qubits always agree. That perfect correlation is the signature of entanglement.

The Shared State

When two qubits are entangled, they share a single quantum state. The most famous example is the Bell State: $|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$

This state says: “There is a 50% chance both qubits are 0, and a 50% chance both qubits are 1.” Crucially, it says there is a 0% chance they are different.

Spooky Correlation

If you take two entangled qubits and move them to opposite sides of the galaxy:

1. You measure your qubit and get a 0.
2. Instantly, the other qubit’s superposition collapses to 0.
3. If a friend measures that distant qubit, they are guaranteed to get a 0.

This happens faster than the speed of light, but it cannot be used to send information faster than light (because the result you get is still random).

Why it matters for Computing

Entanglement is the “glue” of quantum computing. It allows qubits to work together to represent complex relationships that would require a massive number of classical bits. It is the key ingredient in Quantum Teleportation and highly efficient quantum communication protocols.

Takeaways

• Entangled qubits share a single, inseparable quantum state.
• Measuring one qubit instantly determines the outcome of its entangled partner.
• Entanglement enables the massive parallel information processing of quantum computers.