Quantum Computing
Intermediate

Bell State (EPR Pair)

Maximally entangled two-qubit state — measuring one qubit instantly determines the other.

Formula

∣Φ+⟩=12(∣00⟩+∣11⟩)|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)

Variables

|\Phi^+\rangleBell state
|00\rangle, |11\rangleJoint basis states

Example

Measuring qubit 1 as 0 → qubit 2 is also 0, 100 % of the time

Did You Know?

Einstein called entanglement 'spooky action at a distance' — yet it's now used in quantum teleportation experiments worldwide.

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Qubit Superposition State

Intermediate

General state of a single qubit as a superposition of the computational basis states.

Normalisation Constraint

Basic

The squared amplitudes of a qubit must sum to 1, ensuring total probability is 100 %.

Hadamard Gate

Intermediate

Puts a qubit into an equal superposition — the most common single-qubit gate.

Pauli-X Gate (Quantum NOT)

Basic

Flips |0⟩ to |1⟩ and vice versa — the quantum equivalent of a classical NOT gate.

CNOT Gate

Intermediate

Two-qubit gate that flips the target qubit only when the control qubit is |1⟩.

Born Rule (Measurement Probability)

Intermediate

Probability of measuring outcome |k⟩ from a quantum state |ψ⟩.