Bell States
Entanglement, in plain language: two qubits become correlated in a way no classical setup can reproduce — measuring one instantly tells you something certain about the other, no matter how the pair was separated, even though neither qubit had a definite value before measurement (see Measurement and Collapse). It’s not “hidden pre-agreed answers” (that possibility is what Bell tests rule out); the correlation only exists because the two qubits share a single joint state that can’t be factored into two independent single-qubit states — which is also why a two-qubit entangled pair has no single point on any one Bloch Sphere.
The simplest entangled states — 2 qubits, 4 variants:
Base construction: h(0); cx(0,1) → gives |00⟩+|11⟩. Applying an extra X gate (before or after) flips which basis states appear; a Z gate introduces the minus-sign variants (Z Gate and Relative Phase).
Key insight — multiple paths, same state: X can be applied before the circuit (on qubit 1) or after (on qubit 0 or qubit 1) and all three give the same final state, because flipping either qubit of an entangled pair swaps the same basis states. This foreshadows circuit-optimization flexibility used later in Transpilation.
Related
- H Gate, CX Gate and Entanglement
- GHZ States — the N-qubit generalization
- Z Gate and Relative Phase
- Bloch Sphere, Measurement and Collapse
- CHSH Inequality and Bell Tests, Quantum Teleportation, No-Cloning Theorem
Self-Check
- Could you explain entanglement to a friend using the Bell-state correlation, without saying “spooky”?
- Why can’t a Bell state be described as “qubit 0 is in state A and qubit 1 is in state B” separately?
- How do you get from the base Bell state to each of the other three, and which gates does that use?
- If you compute the measurement probabilities for all four Bell states (not just ), what pattern do you see, and why does it follow directly from which basis states each superposition is built from?