Qubit and spin

A qubit is the simplest quantum system: a two-dimensional state space. Susskind’s main physical example is spin, especially a spin with two possible outcomes for any chosen measurement axis.

Plain-language picture

A classical bit is either 0 or 1. A spin measured along z gives either +1 or -1, so it is tempting to treat it like a classical bit. The temptation fails because a state prepared to be definite along z is generally not definite along x or y.

The qubit is therefore not “a bit with unknown value.” It is a state-vector whose components depend on which measurement basis you choose.

Minimal spin basis

Using the z-basis:

|u⟩ = up
|d⟩ = down
|Ψ⟩ = α|u⟩ + β|d⟩

The amplitudes α and β predict z-measurement probabilities by the Born rule.

Why Susskind starts here

Spin is small enough to calculate by hand but strange enough to contain the central quantum lessons: basis dependence, incompatible observables, measurement disturbance, and superposition.

Common pitfalls

  • Do not picture spin as a little arrow with all components already assigned.
  • Do not confuse a two-outcome measurement with a classical two-state hidden variable.
  • Do not ignore the measurement axis.