QVL-27 GHZ: Bell's theorem without inequalities — Quantum 3D Lab

Experiments in the Quantum 3D Lab

• QVL-01 Introduction Lab: meet the qubit — Eight short stations on one qubit: measure, flip, superpose, phase, rotate, interfere, other bases, and a challenge.
• QVL-02 Two qubits side by side — Two independent qubits: four outcomes, and probabilities that multiply.
• QVL-03 The quantum "if": CNOT and the Bell pair — CNOT's truth table, then a Hadamard before it: the Bell pair, where neither qubit has a state of its own.
• QVL-04 Is it really spooky? The CHSH game — A game no classical team wins more than 75 % of the time. Entangled players win 85 %.
• QVL-05 Phase kickback — The control of a controlled gate changes, while the target does not: the trick behind every algorithm.
• QVL-06 Superdense coding — Two classical bits sent with one qubit, thanks to a shared Bell pair.
• QVL-07 Quantum teleportation — A qubit's state moved to another qubit with one Bell pair and two classical bits.
• QVL-08 BB84: a secret key — Two bases, random choices, and an eavesdropper who cannot hide.
• QVL-09 Oracles and reversible logic: a quantum adder — XOR from CNOT, AND from Toffoli, and a half adder that adds every input at once.
• QVL-10 Deutsch–Jozsa: constant or balanced? — One question to the oracle instead of five: the first algorithm faster than any classical one.
• QVL-11 Bernstein–Vazirani: a secret in one look — A hidden bit string read in a single query.
• QVL-12 Grover's search — One marked number in 32, found with 99.9 % certainty after 4 rounds: 109 gates on 5 qubits.
• QVL-13 The quantum Fourier transform — Numbers turned into phases, and patterns into peaks.
• QVL-14 Phase estimation — Reading the phase of a gate to three binary places.
• QVL-15 Shor's algorithm: factoring 15 — The period of 7ˣ mod 15 found on 7 qubits, and from it 15 = 3 × 5.
• QVL-16 Noise and error correction — A bit-flip code on 5 qubits: find the error without looking at the data, and undo it.
• QVL-17 A spin in a magnetic field — Larmor precession, Rabi oscillation and Ramsey fringes: NMR and MRI on one qubit.
• QVL-18 The energy of H₂ (VQE) — A variational quantum eigensolver finds the ground-state energy of the hydrogen molecule.
• QVL-19 Optimisation with QAOA — The best cut of a 4-node network, found by tuning two angles.
• QVL-20 Measurement and collapse: the Stern–Gerlach experiment — Spins through magnets: Born's rule, a second look that always agrees, and an x magnet that wipes out the z answer.
• QVL-21 Wave or particle? The Mach–Zehnder interferometer — One photon, two paths: fringes, a which-path detector that removes them, D² + V² = 1, and Wheeler's delayed choice.
• QVL-22 The delayed-choice quantum eraser — Entangled photons show no fringes, until the idler's path information is erased and the runs are sorted.
• QVL-23 The quantum Zeno effect: a watched qubit never flips — Look often enough and the qubit stays put; look along a turning axis and you drag it along.
• QVL-24 The Elitzur–Vaidman bomb tester — Find a live bomb with a photon that never touches it, and with the Zeno trick almost never set it off.
• QVL-25 Schrödinger's cat and decoherence — An atom, a cat and the air: how records in the environment turn a superposition into what looks like a coin toss.
• QVL-26 Wigner's friend: who collapsed the state? — A friend measures inside a sealed lab; Wigner, outside, can tell collapse from no collapse by undoing her measurement.
• QVL-28 Entanglement swapping: linking qubits that never met — A Bell measurement on the two middle qubits entangles the two outer ones: the heart of a quantum repeater.
• QVL-29 Maxwell's demon and the Szilard engine — A demon that measures lifts a weight with heat alone, until the cost of erasing its memory (Landauer's principle) is paid.
• QVL-30 The quantum walk — A walker with a quantum coin spreads in proportion to the steps, not their square root, and turns classical when the coin is watched.

• Build your own circuit
• Notes: qubits and gates