Quantum Channel Capacity — Hashing Bound

Depolarizing channel: coherent information, hashing bound, capacity vs noise

Channel Parameters

0=Depolarizing, 1=Dephasing, 2=Erasure

Capacity Quantities

Coherent info I_c--
Hashing bound Q_H--
Classical capacity C--
Entanglement-assisted C_ea--
Threshold p_th--
Hashing bound: Q ≥ I_c(ρ,N) = S(B) − S(E)
Depolarizing: N(ρ) = (1−p)ρ + p·I/2
Threshold p_th where Q→0: ~1/4 (depolarizing)
C_ea = S(A) + S(B) − S(A,B) (full entanglement)