A quantum system can exist in a superposition of states until measured. Schrödinger's 1935 thought experiment extends this to macroscopic scales: a cat linked to a quantum decay event is both alive and dead simultaneously — |ψ⟩ = α|alive⟩ + β|dead⟩.
The Bloch sphere visualizes all pure qubit states. The north pole is |0⟩ (alive), south pole is |1⟩ (dead). The equator is maximally superposed. Measurement collapses the state: P(alive) = |α|², P(dead) = |β|².
Decoherence: interaction with the environment entangles the system with countless degrees of freedom, causing the off-diagonal density matrix elements (coherences) to decay exponentially: ρ₀₁(t) = ρ₀₁(0)·e^(-γt). This is why we don't see superpositions of cats in practice.