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

Complete-channel and state-specific error bounds

Complete-channel and state-specific error bounds · lines 1160–1172

For states and compatible finite channels use

d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄} .

The diamond norm includes arbitrary untouched references. Channel pre- and postcomposition are contractive in this norm Watrous.

Displayed formulas in this passage

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$d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄} .$