Every crossing has two faces. The egress face is actual — written, completed, past. The ingress face is potential — unwritten, open, future. Information exists at both levels but with fundamentally different properties.
Classical information lives on the egress face. A classical bit is a completed crossing record: 0 or 1, written, determined. Classical computation sequences egress events causally in \(\tau\).
Quantum information lives on the ingress face — the potential, the unwritten. A qubit is not a written 0 or 1. It is the full bilateral crossing record held open in superposition: both faces potential, neither yet actualised. A quantum gate rotates the ingress-face state without writing it.
| Level | Face | State | Speed limit |
|---|---|---|---|
| \(\infty_0\) potential | Ingress (full) | All crossings superposed | Instantaneous |
| Quantum information | Ingress (structured) | Qubit superposition | Instantaneous within system |
| Classical information | Egress | Written bit: 0 or 1 | \(\leq c\) |
Classical computation operates only on written crossing records. Quantum computation operates on the ingress face before writing. A register of \(n\) qubits holds \(2^n\) potential crossing records simultaneously — one operation on the undivided ingress-face potential of \(\infty_0\). At the end, a measurement (egress event) extracts one written result. The skill of quantum algorithm design is shaping the superposition so that measurement is informative.
Two entangled particles share one bilateral crossing record — one object with two egress faces not yet actualised. The joint ingress-face state is instantaneously coupled. This coupling is real. But it carries no classical information.
Alice controls: which observable she measures; when she measures; which unitary she applies.
Alice does not control: what outcome she gets. The outcome is in the crossing record written at \(\tau_0\). Alice is reading, not writing.
Bob sees: random outcomes regardless of anything Alice does. No pattern is visible without a classical channel.
Quantum teleportation transfers an ingress-face crossing record from Alice to Bob using entanglement plus a classical channel. Neither alone is sufficient.
Entanglement: transfers the ingress-face record instantaneously — but Bob cannot use it without Alice's classical bits.
Classical channel: tells Bob which rotation to apply. Travels at \(\leq c\). The egress-face completion.
No-cloning: the original \(|\psi\rangle\) is destroyed at Alice's end. A crossing record is unique — reading it closes it.
Decoherence is an unwanted egress event — the environment closes a crossing record before the algorithm intends. Error correction encodes one logical qubit across many physical qubits so that partial environmental actualisations can be detected and reversed. The threshold theorem says ingress-face operations can be protected from egress intrusions as long as the intrusion rate is low enough.
Every quantum computation must eventually measure. The ingress face must cash out into egress. This is not a weakness — it is the bilateral structure. The ingress face is powerful precisely because it has not yet been written. The moment it is written it joins the \(\tau\)-ordered causal chain of the physical world.