Manuscript Em03-G@1 · Em03-G-v1.tex · section · 0bb3a8a3

Question, predecessors, and the two release gates

Question, predecessors, and the two release gates · lines 180–261

The principal chain is

qubit input ⟶ ordered compact source interactions ⟶ identified outgoing scalar packet channel ⟶ referenced transmission and recovery bounds .

The operational receiver is a separate chain:

physical scalar field ⟶ local receiver ⟶ quantum memory .

The first chain is constructed here. A coherent local realization of the second chain is not asserted.

Em03-A–C Em03A,Em03B,Em03C provide the selected stationary scalar prescription and finite-packet context. Em03-D Em03D supplies a local bounded-observable architecture. Em03-E Em03E has additional finite radiation payloads. Em03-F Em03F instead identifies source-dependent information in the scalar field itself, but its single-source-observable radiation channel is measure-and-prepare.

Quantum transmission through scalar fields already has explicit nonperturbative protocols in flat and curved spacetimes Simidzija,KasprzakTjoa. We do not claim novelty for its possibility, for controlled displacement, or for the use of noncommuting source observables. Simple-generated qubit–field calculations also have established precedents Tjoa. The present contribution is the stated compact Schwarzschild source realization, its exact interference-bearing packet channel, and its source-input and recovery certificates.

release gates. We distinguish:

Information-theoretic scalar transmission: the identified outgoing packet channel and a mathematical CPTP decoder on that packet;
Local coherent reception: a specified spacetime receiver whose quantum output has a proved referenced comparison with the packet decoder.

Passing the first gate does not pass the second.

boundary. All constructions and estimates are analytical. Compilation, formal verification, numerical execution, calibration, and physical implementation are not asserted. A theorem about a specified effective interaction is not a derivation of its gravitational origin.

. For normal states and channels,

d_{tr} (ρ, τ) = \frac{1}{2} ∥ ρ - τ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥Φ - Ψ ∥_{⋄} .

The channel distance includes arbitrary external references. We use squared pure-target fidelity. In particular,

F_{e} (Λ) = ⟨ Φ ∣ (id_{R} \otimes Λ) (∣ Φ ⟩ ⟨ Φ ∣) ∣ Φ ⟩, ∣ Φ ⟩ = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2} .

Worst-case entanglement fidelity is defined separately in Section sec:recovery.

Displayed formulas in this passage

unlabeled · line 184
$qubit input ⟶ ordered compact source interactions ⟶ identified outgoing scalar packet channel ⟶ referenced transmission and recovery bounds .$
unlabeled · line 197
$physical scalar field ⟶ local receiver ⟶ quantum memory .$
unlabeled · line 246
$d_{tr} (ρ, τ) = \frac{1}{2} ∥ ρ - τ ∥_{1}, d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥Φ - Ψ ∥_{⋄} .$
unlabeled · line 252
$F_{e} (Λ) = ⟨ Φ ∣ (id_{R} \otimes Λ) (∣ Φ ⟩ ⟨ Φ ∣) ∣ Φ ⟩, ∣ Φ ⟩ = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2} .$