Manuscript X-K-ST@1 · X-K-ST.tex · section · 93c39c0f

An exact many-clock law

The multi-instrument composition law › An exact many-clock law · lines 889–903

The joint law is not generally the product of the individual clock marginals. For example,

ρ_{same} = \frac{1}{2} (∣ 00 ⟩ ⟨ 00 ∣ + ∣ 11 ⟩ ⟨ 11 ∣), ρ_{opp} = \frac{1}{2} (∣ 01 ⟩ ⟨ 01 ∣ + ∣ 10 ⟩ ⟨ 10 ∣)

have identical one-clock marginals and disjoint two-clock record laws. Their joint record TV distance is one.

Displayed formulas in this passage

unlabeled · line 894
$ρ_{same} = \frac{1}{2} (∣ 00 ⟩ ⟨ 00 ∣ + ∣ 11 ⟩ ⟨ 11 ∣), ρ_{opp} = \frac{1}{2} (∣ 01 ⟩ ⟨ 01 ∣ + ∣ 10 ⟩ ⟨ 10 ∣)$