Jamming of Nonlocal Correlations

• Jamming of nonlocal correlations is the targeted disruption of multipartite quantum correlations by selectively suppressing higher-order joint distributions while preserving individual marginals.
• The operational no-signalling framework formalizes jamming by ensuring changes in joint output statistics do not enable superluminal communication, as demonstrated in both Minkowski and curved spacetimes.
• In quantum networks and Bell scenarios, jamming affects protocols like device-independent key distribution by degrading stronger correlations first, prompting a reevaluation of cryptographic security measures.

Jamming of nonlocal correlations refers to a suite of phenomena, mechanisms, and constraints by which multipartite nonlocal or quantum correlations are altered, suppressed, or constrained—yet without introducing operational superluminal signalling. Jamming arises in quantum networks, Bell-like scenarios, and relativistic spacetime settings, and is now formalized through operational no-signalling (ONS): mechanisms that can remotely modify joint higher-order correlations, but not the individual marginals, in ways that do not allow faster-than-light communication. The sharp distinction between the jamming of dynamical or nonlocal correlations and the preservation of local observables is crucial across quantum information, network nonlocality, and the foundations of relativistic causality.

1. Foundational Notions: Nonlocal Correlations and Jamming

Nonlocal correlations are those between spacelike separated parties which cannot be explained by local hidden variable models, and are typically witnessed in quantum protocols via violations of Bell or network inequalities. In multipartite or networked scenarios, nonlocal correlations appear not just in bipartite marginal distributions but in higher-order joint distributions across multiple parties. Jamming is the targeted disruption—through noise, network constraints, or relativistic causal structures—of these nonlocal, often higher-order, correlations, without affecting operationally accessible single-site statistics or enabling superluminal transmission of information.

A canonical example is the tripartite “jamming” box, where a third party (“jammer”) can choose an input that modifies the joint distribution of two remote outcomes, such that

$$P(A=a\mid X=x) = P(A=a\mid X=x') \ P(C=c\mid X=x) = P(C=c\mid X=x') \ P(A=a, C=c\mid X=x) \ne P(A=a, C=c\mid X=x')$$

for all $x\ne x'$, but with the marginal distributions on $A$ and $C$ individually invariant—ensuring operational no-signalling (Eckstein et al., 29 Dec 2025, Vilasini et al., 2023).

2. Formal Frameworks: Operational No-Signalling and Relativistic Causality

The operational no-signalling (ONS) framework delivers a rigorous criterion for physicality in the presence of jamming. In this setting, $n$ agents are assigned input spacetime random variables (SRVs) $(X_i, p_i)$ and output SRVs $(A_i, q_i)$, with $p_i\prec q_i$ (causal order). The joint conditional statistics

$$P((a_1, q_1), \dots, (a_n, q_n) \mid (x_1, p_1), \dots, (x_n, p_n))$$

are ONS-compliant iff, for every subset pairing $(F, G)$ such that the outputs $q^G$ are operationally separated from inputs $p^F$, the conditional output statistics in $G$ are invariant under choices of the $F$-inputs.

The crucial insight is that jamming—i.e., the possibility that a remote agent's choice modifies only a high-order joint output outside their causal future—is compatible with all ONS constraints and hence does not equate to operationally detectable superluminal signalling. This refutes previous claims that jamming inherently implies unphysical causal effects (Eckstein et al., 29 Dec 2025).

In spacetime settings, geometric constructions permit the simultaneous ONS-legal jamming of $n$-party joint statistics while leaving all proper subset marginals untouched, through holographic arrangement of the agents' future light cones (Eckstein et al., 29 Dec 2025). In black hole spacetimes, the absence of gathering points for spacelike-separated outputs similarly permits jamming of horizon-crossing nonlocal correlations without operational signallability.

3. Jamming in Quantum Networks and Bell Scenarios

In network nonlocality, jamming manifests as constraints on the region of achievable correlators imposed by assumptions such as no-signalling and source independence (NSI). As shown in the triangle network (Gisin et al., 2019), explicit inflation techniques and the derivation of NSI inequalities “jam” classical (local) correlations, carving out subsets of the correlator space that cannot be attained by classical trilocal models. While quantum and certain post-quantum correlations may lie within this region, explicit points exist where NSI constraints are provably tight, and others (“gap regions”) where jamming may capture truly nonclassical, nontrilocal, or even post-quantum correlations.

Jamming in the context of Bell scenarios is formalized via relaxations of standard no-signalling (NS) conditions (Vilasini et al., 2023). For example, in a tripartite Bell experiment, standard NS3 requires independence of all two-party marginals from the third party's input. Jamming relaxes this so that only certain two-party marginals must be invariant, permitting the “jammer” to affect high-order joint distributions nonlocally, again without locally observable signalling.

4. Mechanisms: Noise Channels and Hierarchies of Correlation Dilapidation

A distinct aspect of jamming emerges in the context of dynamical decoherence and noise. In two-qubit quantum systems undergoing amplitude-damping, phase-damping, or depolarizing channels, higher-order nonlocal correlations (e.g., those witnessing non-LHV behaviour or Bell-CHSH violation) are “jammed” or destroyed at lower noise strengths than teleportational utility or simple entanglement (Paulson et al., 2015). This strict hierarchy—$$\varepsilon_{LHV} \leq \varepsilon_{Bell} \leq \varepsilon_{Tel} \leq \varepsilon_{Ent}$$ for critical noise parameters—implies that as noise increases, stronger forms of nonlocality are precluded first. Similar ordering persists in maximally entangled mixed states and Werner states.

The implication in quantum communication and cryptographic settings is that various protocols (e.g., device-independent QKD, teleportation, entanglement-witnessing) have differing sensitivity to jamming: protocols predicated on stronger forms of nonlocality fail at lower noise, while minimal entanglement remains more robust (Paulson et al., 2015).

5. Jamming versus Superluminal Signalling: Controversies and Clarifications

Misconceptions have arisen regarding the physical admissibility of jamming mechanisms, particularly whether any physical implementation necessarily implies superluminal communication or causal loops. Analyses based on operational no-signalling have demonstrated that so long as marginal and conditional statistics on spacelike-separated outputs remain invariant under changes to operationally separated inputs, no protocol for extracting superluminal signalling exists—even when high-order correlations are jammed (Eckstein et al., 29 Dec 2025).

However, causal-modeling analyses reveal that certain jamming constructs necessarily require hidden superluminal fine-tuning (unfaithful causal graphs), raising problems for embedding such theories in a causal framework unless fundamental “hidden” variables are truly inaccessible (Vilasini et al., 2023). The distinction is thus between operational (observable) signallability and underlying causal structure: jamming per se is ONS-legal, but may be ruled “unphysical” on hidden causal grounds unless protected by inaccessibility of ancillary systems.

6. Physical Realizations and Geometric Constraints

ONS-legal jamming has concrete realizations in Minkowski and curved spacetimes. In Minkowski space, via appropriate placement of sender and $n$ receiver points, one constructs scenarios in which the sender can jam the $n$-party joint correlation, all while each individual or $(n-1)$-tuple marginal remains unjammed (Eckstein et al., 29 Dec 2025). These constructions crucially depend on the geometry of light cones and the existence (or not) of gathering points for spacetime events.

In black hole spacetimes, gathering points for cross-horizon events may not exist, enabling the jamming of correlations between parties separated by event horizons—again, without possibility of extracting operational superluminal signalling (Eckstein et al., 29 Dec 2025).

7. Operational Consequences and Applications

Jamming mechanisms have critical implications for quantum information, particularly for protocols relying on joint statistics rather than single-party marginals. Randomness generation, device-independent key distribution, and large-memory nonlocal games can be broken, or their security weakened, if adversarial jamming occurs at the level of $n$-joint correlations without locally detectable disturbance. Honest parties may be forced to exchange or aggregate outputs at a common future point to detect and counter such tampering.

No communication complexity or cryptographic security can be built upon an assumption of standard no-signalling alone; higher-order ONS constraints and causal-modeling checks are essential to preclude subtle or hidden jamming channels (Eckstein et al., 29 Dec 2025, Vilasini et al., 2023).

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In summary, jamming of nonlocal correlations formalizes the selective, symmetry- and causality-preserving suppression of higher-order quantum or classical correlations, fully consistent with operational no-signalling and relativistic causality, but subject to fine-tuning pathologies in certain causal models unless hidden subsystems are fundamentally inaccessible. The ONS framework provides the definitive operational standard for distinguishing physically admissible jamming from truly unphysical (i.e., superluminally signallable) processes, with broad implications ranging from quantum network security to the structure of correlations in curved spacetime (Eckstein et al., 29 Dec 2025, Vilasini et al., 2023, Paulson et al., 2015, Gisin et al., 2019).