Communication Through Quantum Fields

A field communication channel is induced by a localized encoder, field propagation, a localized receiver, and a readout. Nonzero vacuum correlations do not by themselves transmit a message. The channel depends on the coupling schedules, field state, energy budget, mode matching, and causal relation between sender and receiver.

Required background. Algebraically localized operations defines supported encoders and receivers. Infinite-dimensional channel–state methods supplies the domain restrictions needed for bosonic fields.

Helpful background. Thermal states and the KMS condition supplies thermal-noise structure. Localized detector models supplies a concrete transducer.

Sender–field–receiver channel

Prepare a sender system $S$, field state $\rho_F$, and receiver state $\sigma_R$. Let $U_S$ and $U_R$ be unitaries generated by compactly supported couplings, with $U_R$ later in causal order. The induced receiver channel is

$$\mathcal N(\rho_S)=\operatorname{tr}_{S,F}\!\left[ U_RU_S(\rho_S\otimes\rho_F\otimes\sigma_R) U_S^\dagger U_R^\dagger \right].$$

Every symbol in this expression is physical protocol data. Changing the receiver gap, wavepacket, switching, or decoding observable changes $\mathcal N$.

For a classical bit $a$, choose encoders $\mathcal E_a^S$ and readout effects $E_y^R$. Then

$$p(y\mid a)=\operatorname{tr}[E_y^R\mathcal N(\rho_a)]$$

defines the classical channel actually used. Its one-shot error, mutual information for a chosen prior, and asymptotic capacity are different quantities.

The physical channel is the full sender–field–receiver composition. Propagation alone does not specify an input alphabet, receiver mode, or error criterion. The diagram is schematic.

Causal and mode-matching controls

Move the receiver coupling outside the causal future of the sender while keeping the initial field state fixed. A localized protocol must make $p(y\mid a)$ independent of $a$, although receiver noise and correlations with sender apparatus may remain. This null geometry tests the signaling term.

Next keep the causal geometry but replace the matched receiver smearing by an orthogonal or detuned profile. The channel contrast should decrease according to the wavepacket overlap. If a capacity estimate remains unchanged, the calculation may be using an ideal global mode rather than the declared localized receiver.

In perturbative detector models, signal terms and local noise often enter at comparable orders. Quote the regime where probabilities remain normalized and where neglected terms are smaller than the code’s error margin. Cliche and Kempf 2010, §§ III–V construct the resulting relativistic quantum channel explicitly. Tjoa and Gallock-Yoshimura 2022, §§ III–VI analyze rapidly interacting detector channels beyond a slow-switching picture.

A wavepacket qubit

In a regulated free field, encode a logical qubit in the vacuum and a normalized wavepacket excitation,

$$|0_L\rangle=|0\rangle, \qquad |1_L\rangle=a^\dagger(h)|0\rangle.$$

A receiver matched to $h$ through a physically supported filter sees loss, added noise, and finite-time distortion. Report the packet normalization, energy $\langle H\rangle$, bandwidth, tail tolerance, and overlap with the receiver. A plane wave has sharp momentum but is not a localized message.

Receiver mode mismatch and localization tails can invalidate a channel model independently of relativistic causal support. Both must be bounded before a rate is quoted. The map is schematic.

References

• 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.