This table shows a two-qubit result where the joint outcomes carry the pattern: zero-zero and one-one each get probability 1/2, while the crossed rows get 0. The same-bit probability adds to 1, but each single bit is still uncertain, so the visual table is about joint evidence rather than separate hidden guesses. Real experiments estimate these probabilities from finite shots, calibration choices, basis alignment, readout errors, and uncertainty.
The joint probability table shows same-bit correlation while each single bit remains uncertain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Only two joint outcomes have probability
The joint measurement distribution has probability one half on zero-zero and one half on one-one. The crossed outcomes have probability zero.
outcome∣0,0⟩∣0,1⟩∣1,0⟩∣1,1⟩P210021
The bit values always match in this basis
Add the rows where the two bit values match. The same-bit probability is one, even though each individual bit is still uncertain.
Psame=21+21=1
The table separates joint and marginal facts
The joint table says both bits match. It does not say either single qubit had a known value before measurement.