SUPERPOSITION

Amplitudes are arrows

Length The length squared is the probability.

Direction The phase: invisible to one measurement, but it decides what cancels later.

|+⟩ and |−⟩ The same 50/50 odds, but opposite phases, so they behave differently.

Probabilities alone don't describe a qubit: the phase matters too.

MEASUREMENT

Measuring collapses the state

Before The arrow can point anywhere between |0⟩ and |1⟩.

During You get 0 with probability cos²(θ/2), otherwise 1.

After The arrow jumps to the result: measure again and you get the same answer.

Measurement isn't passive: it changes the qubit.

CHOOSING WHAT TO MEASURE

Measure along Z |+⟩ gives 0 or 1 at random.

Measure along X |+⟩ gives + every time.

In practice You rotate the qubit, then measure along Z.

Quantum key distribution uses this to reveal any eavesdropper.

THE WORLD IS WATCHING

Decoherence Any interaction that leaks information acts like a measurement.

The culprits Stray photons, vibrations, defects in the chip, heat.

The defence Cold, dark, shielded fridges and very clean materials.

Keeping a qubit quantum means keeping the universe from noticing it.

NO COPIES

The no-cloning theorem No device can make a perfect copy of an unknown quantum state.

So No backups, and no peeking at a copy instead of the original.

But Error correction can still protect qubits, by spreading information across many of them.

This is why quantum error correction needs clever tricks rather than simple copies.

UNIT 5 STUDY COMPLETE

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You've seen how amplitudes set the odds, how measurement collapses a qubit, and why qubits can't be copied.