It is tempting to attach "quantum" to a codec. The theory does not support it,
and the theorem that refuses is worth more than the claim would be, so this
computes the limits instead of promising to beat them.
quantum_source adds von Neumann entropy S(rho), the Schumacher limit for a
quantum source, and the Holevo bound chi on an ensemble. The tests state the
consequences rather than assert the formulas: a pure state carries no entropy
and is fully compressible; half a Bell pair is maximally mixed and costs exactly
one qubit, the entropy a state vector could not report; orthogonal states carry
a full bit, non-orthogonal ones lose part of it permanently for every
measurement anyone will ever build; and no ensemble beats one bit per qubit.
That last is the useful one -- n qubits carry at most n classical bits, so
quantum is not a smaller pipe for classical media. Where it genuinely wins is
protocols, not codecs.
Eigenvalues come from a real Jacobi sweep on the doubled matrix [[A,-B],[B,A]],
whose spectrum is the Hermitian one twice over, keeping to the +-*/sqrt
discipline quantum_mps sets. Entropy needs a logarithm and libm differs between
platforms, so log2 is computed here by repeated squaring -- multiply and compare
only -- and the results are bit-reproducible rather than merely close.
Also records the 2030 transport landscape survey behind this decision.
Co-Authored-By: Claude Opus 5 <[email protected]>
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