Entanglement

Quantum entanglement occurs when two or more qubits become correlated in such a way that the state of one instantly determines the state of the other, regardless of distance.

Einstein famously called this "spooky action at a distance."

Example: Bell State

|Φ+⟩ = (|00⟩ + |11⟩)/√2

If you measure the first qubit and get |0⟩, the second qubit is guaranteed to be |0⟩. If you get |1⟩, the second is |1⟩.

The simplest way to create entanglement uses two gates:

1. Apply H to qubit 0 → creates superposition

2. Apply CNOT with control=0, target=1 → creates entanglement

This produces the Bell state: (|00⟩ + |11⟩)/√2

Try it in the Circuit Builder!

Start with 2 qubits, apply H to q0, then CNOT from q0 to q1. Notice how the probabilities show only |00⟩ and |11⟩, each at 50%.

Entanglement is essential for:

• Quantum teleportation — transferring quantum states

• Quantum key distribution — unbreakable encryption

• Quantum error correction — protecting quantum information

• Quantum algorithms — achieving speedups like in Shor's and Grover's algorithms

Entanglement is considered the key resource that makes quantum computing fundamentally more powerful than classical computing.