Quantum Superposition: How Particles Exist in Multiple States

Part 1: The Double-Slit Experiment

When single photons or electrons are fired one at a time through two parallel slits, they do not create two neat lines like bullets would. They create an interference pattern of bright and dark fringes on the detector, proving each particle passes through both slits simultaneously as a probability wave.

Part 2: Mathematical Representation of Qubits

1. 1. State Vectors: A classical bit is either |0> or |1>. A quantum qubit is represented as |Psi> = alpha|0> + beta|1>.
2. 2. Complex Amplitudes: Alpha and beta are complex numbers whose squared magnitudes (|alpha|^2 + |beta|^2) equal exactly 1.
3. 3. Unitary Transformations: Quantum logic gates rotate this vector along the surface of a geometric Bloch sphere without collapsing it.
4. 4. Decoherence: Stray interactions with thermal noise or stray photons cause phase interference to decay into classical uncertainty.

Part 3: Quantum Computing & Cryptographic Implications

Superconducting quantum processors (IBM, Google) leverage 100+ entangled qubits in cryogenic dilution refrigerators, executing algorithms across 2^100 states simultaneously.