Causal Channels and Relativistic Communication

Relativistic communication is a task defined by localized interventions, causal geometry, a field-mediated channel, energy and bandwidth constraints, and an error criterion. Vacuum correlations, entanglement, signaling, and channel capacity are different resources or properties. This chapter separates them before analyzing transmission, harvesting, and Bell protocols in flat-spacetime QFT.

Helpful background. Causal quantum channels supplies localized CP maps, data processing supplies operational distinguishability bounds, and Lindblad field dynamics supplies a comparison for physical noise. The measurement–correlator claim contract is useful when a protocol is connected to experimental evidence.

Enter this chapter

Start with signaling and causal composition, which defines influence by interventions rather than correlations. Algebraically localized operations turns that definition into a representation-independent action criterion. Channel–state methods in infinite dimensions explains why a finite-dimensional maximally entangled Choi vector cannot simply be imported into a type-III local algebra.

Then construct an actual field communication channel from sender and receiver couplings. The subsequent routes distinguish quantum communication and entanglement distribution, entanglement harvesting, and pre-existing correlation versus causal exchange. Finish with energy-constrained capacities, wavepacket and frame choices, Bell nonlocality, and the dated protocol status comparison.

One physical field setup supports several inequivalent tasks. Each task has its own resource, success criterion, and causal interpretation; a nonzero correlator is not itself a communication channel. The diagram is schematic and not to scale.

Correlation is not influence

Let $a$ denote a sender’s intervention choice and $y$ the receiver’s outcome. Operational signaling is present when

$$p(y\mid a)\ne p(y\mid a')$$

for some choices $a,a'$, with the preparation and receiver operation held fixed and uncommunicated outcomes averaged. A correlation $p(x,y)\ne p(x)p(y)$ can instead arise from a common cause or an entangled initial field state. Microcausality and localization imply no signaling for spacelike-supported interventions even though vacuum correlations are generally nonzero.

The distinction propagates into information measures. Mutual information between two probe records quantifies correlation in their joint distribution. Classical capacity asks for an asymptotic reliable coding rate under a specified input constraint. Quantum capacity asks for coherent transmission. Entanglement harvesting asks whether localized probes become entangled through interaction with the field, with causal exchange excluded if the claim is specifically about pre-existing spacelike correlations; Pozas-Kerstjens and Martín-Martínez 2015, §§ II–IV give a controlled detector calculation. Bell violation is yet another statement: local QFT can support maximal spacelike Bell correlations while still forbidding signaling, as established under the hypotheses of Summers and Werner 1987, Theorems 3.1 and 4.1, pp. 252–257.

A common protocol comparison

Relativistic communication tasks, their resources, and decisive failure tests

Protocol	Supported operations	Channel or resource	Energy and coding constraint	Signaling test	Licensed output	Principal failure test
Spacelike detector pair	Two compact local couplings	Initial field correlations	Fixed gaps, profiles, perturbative order	Receiver marginal invariant under sender choice	Correlation or harvesting witness	Remove support tails and compare with a separable field control
Timelike bit transmission	Local encoding and later readout	Induced classical channel p(y | a)	Input alphabet, duration, mean energy	Nonzero intervention contrast inside light cone	One-shot error or achievable classical rate	Move receiver outside causal future
Qubit or entanglement transmission	Coherent encoding, channel, decoder	Quantum channel 𝒩	Code block, energy, bandwidth, fidelity error	Causal support of every encoder and decoder	Entanglement fidelity or quantum-rate bound	Remove phase reference or count rare heralds honestly
Bosonic wavepacket coding	Mode preparation and matched receiver	Lossy or noisy bosonic channel	Mean or peak energy plus bandwidth	Retarded support and receiver mode overlap	Task-specific constrained capacity	Change the constraint or admit localization tails
Bell test in two field regions	Random local settings and bounded readouts	Nonlocal correlation, not signaling	Detection efficiency and trial definition	No setting changes remote marginal	Loophole-aware CHSH violation	Add postselection, setting correlation, or support overlap
Broadcast field channel	One sender and multiple localized receivers	Quantum broadcast map	Energy, timing, receiver geometry	Each marginal respects causal order	Achievable multicast or entanglement-assisted rates	Confuse pairwise correlations with simultaneous decodability

The table deliberately does not put all protocols on one scalar readiness axis. An algebraic theorem, a perturbative detector calculation, a numerical capacity bound, and a hardware demonstration are different kinds of evidence.

Field channels and constraints

A sender $S$ prepares or couples a localized degree of freedom to the field, and a receiver $R$ later couples and reads out. Tracing over inaccessible field and apparatus degrees of freedom produces an induced channel

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

The channel is meaningful only with $U_S,U_R$, the field state, and the receiver readout fixed. In detector models, spacelike separation removes the signaling term while leaving correlations possible. Timelike coupling can yield a nonzero classical channel, as shown explicitly by Cliche and Kempf 2010, §§ III–V. Rapid-interaction models can sometimes be treated nonperturbatively, but their capacities remain properties of the declared channel and constraint, not of “the field” universally; see Tjoa and Gallock-Yoshimura 2022, §§ III–VI.

Correlation, causal exchange, and reliable communication require increasingly specific intervention data. Energy, localization, coding, and accessible-record checks can independently downgrade the conclusion. The map is schematic.

Infinite-dimensional capacities require a constraint such as $\operatorname{tr}(H\rho)\le E$; without it, even continuity and compactness properties can fail. The explicit energy-constrained field-channel analysis of Barcellos and Landulfo 2021, §§ III–VI illustrates how both the channel and its cost must be fixed. Wavepacket localization adds a second control: exactly band-limited positive-frequency modes cannot also have compact spacetime support. Report the tail norm or operational receiver mismatch instead of treating plane waves as messages.

Review the chapter

After these routes you should be able to distinguish correlation from intervention influence; write a localized sender–field–receiver channel; state which capacity and constraint are being used; separate harvesting from causal exchange; identify frame- and mode-dependent quantities; and design a Bell or communication claim that remains valid after postselection and support-tail tests.

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.
• Pozas-Kerstjens, A., and Martín-Martínez, E. (2015). “Harvesting Correlations from the Quantum Vacuum.” Physical Review D 92, 064042. DOI. Open PDF.
• Summers, S. J., and Werner, R. (1987). “Maximal Violation of Bell’s Inequalities Is Generic in Quantum Field Theory.” Communications in Mathematical Physics 110, 247–259. DOI.
• Tjoa, E., and Gallock-Yoshimura, K. (2022). “Channel Capacity of Relativistic Quantum Communication with Rapid Interaction.” Physical Review D 105, 085011. DOI. Open PDF.