Communication-constrained nonlocal correlations

Abstract

Identifying the physical grounds distinguishing quantum theory from broader probabilistic frameworks remains an open challenge. Communication-based proposals -- most notably the principles of impossibility of superluminal signaling and information causality (IC) -- highlight the role of communication in ruling out unphysical theories and offer an operational rationale on why quantum predictions prevail over these alternative models. Nevertheless, most such developments rely on communicating parts optimizing over specific tasks, such as communication complexity problems and random access codes (RAC). In this work, we systematically extend this communication-based approach. We characterize the class of communication tasks relevant for this context, and employ the general information-theoretic framework to derive new operational constraints preventing such unphysical behaviors. Remarkably, our results reveal a broad family of previously undetected implausible behaviors, independent of any particular encoding or decoding strategy, reinforcing the role of communication as a fundamental lens through which physically meaningful theories can be identified.

Figures (3)

• Figure 1: Causal structure associated with general communication scenarios. The parties share a no-signaling (NS) resource $\mu_{\text{NS}}$, which assists Alice in preparing a classical message $A$ that encodes the initial data $X$. Upon receiving the message and supported by the shared resource, Bob produces an outcome $B$ based on a randomly selected input $Y$.
• Figure 2: Causal structure associated with general communication scenarios depicted in Fig. \ref{['fig:noiseless']}, extended to include classical noisy communication specified by $\epsilon$, yielding the effective message $A'$ received by Bob.
• Figure 3: Causal structure considering three sources of uncertainty: $X_0, X_1$ and the classical communicating channel specified by $\epsilon$.