quantumCapacities
plain-language theorem explainer
Enumerates the four standard quantum-channel capacity notions (classical C, quantum Q, entanglement-assisted C_E, private) as a string checklist. Information theorists working the RS ledger-bandwidth program would cite it as the quantum side of the capacity taxonomy. The body is a bare list literal, not a derived bound.
Claim. A fixed list of four capacity labels for quantum channels: (i) classical capacity $C$ with $C \le \log d$ in dimension $d$; (ii) quantum capacity $Q$ tied to coherent information; (iii) entanglement-assisted capacity $C_E = 2C$ when shared ebits are available; (iv) private capacity for secure communication. In the RS reading these rates are constrained by the eight-tick phase structure.
background
Module INFO-002 aims to derive Shannon channel capacity from Recognition Science ledger bandwidth. Classically, $C = \max_{p(x)} I(X;Y)$ bits per use, and for a Gaussian channel $C = \tfrac12\log_2(1+S/N)$. The ledger supplies a fundamental record/transmit rate that is meant to force these formulas.
Sibling definitions already cover classical mutual information, nonnegativity and symmetry, the capacity functional, a uniform input distribution, and a Shannon theorem stub. The present entry extends that taxonomy to the quantum setting, where several inequivalent capacities coexist (Holevo classical capacity, coherent-information quantum capacity, entanglement-assisted capacity, private capacity).
Upstream entropy notions in the repo (configuration defect entropy, horizon microstate log-count, Boltzmann entropy) supply the $S$ that appears in Holevo information $\chi = S(\rho)-\sum_x p_x S(\rho_x)$, but this definition does not yet wire those objects in.
proof idea
Definitional list literal. No tactics, no lemmas, no algebraic reduction: four hard-coded strings naming the standard capacity species. The adjacent Holevo-bound comment ($C \le \chi$ with von Neumann $S$) is documentation for a neighboring declaration, not part of this body.
why it matters
Places the quantum capacity zoo inside the INFO-002 ledger-bandwidth program so later theorems can state which RS rate bounds which capacity. The doc-comment ties the list to the eight-tick octave (forcing-chain T7, period $2^3$), the natural phase clock that should limit how fast the ledger can write quantum information.
No downstream consumers yet (used_by is empty), so this is taxonomy scaffolding rather than a proved bound. It does not itself invoke J-cost, RCL, or the mass ladder; those enter only when a future theorem converts eight-tick bandwidth into a concrete $C$, $Q$, or $C_E$ inequality.
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