The Formula

Why This Matters to Physics

Quantum information theory asks: how much information can a single photon carry? The standard answer involves Holevo’s bound, which is abstract and hard to apply. This deposition gives an engineering answer: count the resolvable states in each physical degree of freedom (wavelength, polarization, intensity), take the floor-log of each, and add them up. The result is exact, not approximate, and directly computable from detector specs.

Why This Matters to Optical Computing

Every optical interconnect — fiber, waveguide, free-space — ultimately carries photons. This formula sets the hard ceiling: no encoding scheme can exceed C(λ,θ,I) bits per photon. A designer who knows their detector’s wavelength resolution (δλ), angular resolution (δθ), and dynamic range (I_max/I_min) can immediately compute the maximum bandwidth without building anything.

For example, a silicon photonic detector with:
• Δλ = 100nm bandwidth, δλ = 0.1nm resolution → 10 bits
• δθ = 1° polarization resolution → 8.5 bits
• 60dB dynamic range → 20 bits
Total: 38.5 bits per photon. At 10 GHz modulation, that is 385 Gbps per waveguide.

Why This Matters to AutoPhi

The AutoPhi architecture uses optical voxel interconnects at the higher process nodes (14nm Peak and above). The photon chromosome formula sets the bandwidth ceiling for these links. At the 1.5nm AQCHS node, the interconnects switch to direct quantum coupling (entanglement-based, not photonic), but for 90% of the product line, this formula governs.

The Biological Metaphor

We call it a ‘chromosome’ because a biological chromosome carries information in discrete genes arranged along a linear structure. A photon carries information in discrete channels (wavelength, polarization, intensity) arranged along its physical degrees of freedom. The analogy is not poetic — it is structural. Both are information carriers with finite, countable capacity determined by resolution limits.

Practical Applications

• Optical network design: Compute maximum throughput before selecting hardware.
• Quantum key distribution: The formula bounds the maximum key rate per photon in QKD systems like BB84.
• Astronomical spectroscopy: The wavelength term sets the information content of stellar spectra, enabling optimal telescope detector design.
• LiDAR systems: The intensity term determines the maximum depth resolution of time-of-flight sensors.