Quantum Communication and Entanglement Distribution

Quantum communication requires preservation of coherence, not merely a visible classical signal. A field-mediated protocol must specify an encoding, localized physical channel, decoder, energy and timing constraints, and a fidelity or asymptotic error criterion. Entanglement distribution additionally requires honest accounting of pre-shared correlations, phase references, heralding probability, and classical records.

Required background. Field communication constructs the sender–field–receiver channel.

Helpful background. Energy-constrained channel distances supplies a physically meaningful error measure for bosonic inputs.

Entanglement transmission test

Let $R$ be a reference and $S$ the encoded system. Prepare a maximally entangled logical state $|\Phi\rangle_{RS}$ within a finite-energy code subspace, send $S$ through $\mathcal D\circ\mathcal N\circ\mathcal E$, and compute

$$F_e=\langle\Phi| (\operatorname{id}_R\otimes\mathcal D\circ\mathcal N\circ\mathcal E) (|\Phi\rangle\langle\Phi|) |\Phi\rangle.$$

High $F_e$ tests coherent transmission on that code. A large classical contrast between two codewords does not imply high $F_e$: dephasing can preserve a classical bit while destroying every superposition.

Quantum transmission and entanglement distribution share the physical channel but use coherence-sensitive success criteria. They are not certified by the signaling branch alone. The diagram is schematic.

Lossy wavepacket example

For a single matched bosonic wavepacket with transmissivity $\eta$ and environment mode $e$,

$$a_{\mathrm{out}}=\sqrt\eta\,a_{\mathrm{in}} +\sqrt{1-\eta}\,e.$$

Encode one half of a finite-energy entangled pair into the input mode. Loss and thermal occupation of $e$ reduce the entanglement fidelity. The actual $\eta$ must be derived from localized mode overlap and propagation, not inserted as a global plane-wave parameter.

If success is heralded, the relevant resource rate includes the success probability $p_s$. A branch fidelity $F_e^{(s)}$ can approach one while $p_s\to0$; the useful yield per trial or per unit time can still vanish. Include detector reset, classical herald communication, and discarded trials in comparisons.

Phase references and pre-shared resources

A single-rail code $\alpha|0\rangle+\beta|1_h\rangle$ requires a phase reference to access the coherence. Removing that reference can twirl the state over a $U(1)$ phase and reduce the operational channel. Likewise, vacuum entanglement present before the protocol is a resource of the initial field state; it cannot be counted again as newly distributed entanglement unless the task definition permits consumption of that resource and measures the net change.

Detector-channel models demonstrate that localized field couplings can define classical communication channels Cliche and Kempf 2010, §§ III–V and, in rapid-interaction regimes, energy-constrained quantum channels Tjoa and Gallock-Yoshimura 2022, §§ III–VI. Barcellos and Landulfo 2021, §§ III–VI also separate communication energy from switching and background contributions. These are controlled theoretical models, not universal platform performance claims.

Rare heralding, omitted reference frames, and double-counted initial correlations can each inflate an entanglement-distribution claim without changing the underlying physical channel. The map is schematic.

Evidence boundary

As assessed through 2026-08-10, the representative results cited here establish analytic or numerical performance of specified detector and wavepacket models. They do not by themselves demonstrate a scalable flat-spacetime field transducer with fault-tolerant quantum rate. Report theorem, model calculation, simulation, and experimental realization as distinct evidence levels.

References

• Barcellos, I. B., and Landulfo, A. G. S. (2021). “Relativistic Quantum Communication: Energy Cost and Channel Capacities.” Physical Review D 104, 105018. DOI. Open PDF.
• Cliche, M., and Kempf, A. (2010). “The Relativistic Quantum Channel of Communication through Field Quanta.” Physical Review A 81, 012330. DOI. Open PDF.
• Tjoa, E., and Gallock-Yoshimura, K. (2022). “Channel Capacity of Relativistic Quantum Communication with Rapid Interaction.” Physical Review D 105, 085011. DOI. Open PDF.