CS639
Back to notesQuantum communication
Joint outcomes
+ / − are the chosen axis’s eigenstatesAlice ↓ / Bob →+−Alice alone
+
50.0%same
0%different
−
Bob alone0%different
50.0%same
Same outcomes100%
Correlation ⟨AB⟩1
Perfect agreement in these bases.
Bob’s local state
Before / after learning Alice’s resultAll runsmaximally mixed
x
y
z
Without Alice’s outcome, Bob sees I/2 in every basis. Changing her analyzer cannot send him a message.
What distinguishes the mixture?
The mixture picks |00⟩ or |11⟩ with equal probability. It agrees with Φ⁺ in Z, but gives all four X outcomes equally. Φ⁺ retains a relative phase between its two terms, so the X outcomes stay correlated. For Φ⁺, Y outcomes are opposite: the complex phases matter.
Here θ is measured down from +Z and φ around from +X toward +Y. The signs + and − mean eigenvalues +1 and −1; for Z they are |0⟩ and |1⟩.