04 · Two qubits
Entanglement
Some states of a pair cannot be written as “this one times that one.” Measuring one updates the description of the other because there was never two descriptions.
In English
Two qubits can share one description that does not split into “qubit A’s state times qubit B’s state.” Measure A and you instantly know B — not because a signal flew, but because there were never two separate stories.
- Try this
- Make a Bell pair. Measure the left qubit a few times. The right one always matches. That correlation is the resource.
- Keep this
- Entanglement is one state for two qubits, not a wire between them.
Lab · two qubits, one vector
0.71|00⟩ + 0.71|11⟩
Qubit 0 is the left bit in |q0 q1⟩
|00⟩0.7150%|10⟩00%|01⟩00%|11⟩0.7150%
A product state factors: |ψ⟩⊗|φ⟩. An entangled state does not. The pair has a description; the pieces do not, except as a mixed state if you ignore the other.
Measuring one qubit of Φ⁺ does not send a bit faster than light. It updates your description of a system you already shared. The correlations are stronger than any shared random coin — that is Bell’s point — but they still need a comparison of records.