Local perception operators and classicality: new tools for old tests

TL;DR

This work introduces Local Perception Operators (LPOs) to reduce global quantum observables to locally accessible statistics, enabling locality tests beyond standard Bell-CHSH violations. It defines two LPO-based witnesses, an asymmetric one that provides a sufficient LHV-compatible bound computable from local data, and a symmetric one that is nonlinear and state-dependent, yielding geometry-driven upper bounds. Numerical results show that LPO witnesses can reveal nonlocality in regimes where conventional tests fail and extend to multipartite scenarios, with explicit analyses of I3322-type inequalities and tripartite states. The framework offers an operational alternative to violation-based locality tests and opens avenues to connect locality with entanglement and contextuality in more complex quantum systems.

Abstract

Quantum nonlocality is often judged by violations of Bell-type inequalities for a given state. The computation of such violations is a global task, requiring evaluation of global correlations and subsequent testing against a Bell functional. We ask instead: when is a given state local (classical)? We formalize this question via local perception operators (LPOs) that compress global observables into locally accessible statistics, and we derive two complementary witnesses -- one implementable by a single party with classical side information, one intrinsically two-sided. These tools revisit familiar Bell scenarios from a new operational angle. We show how the witness leads to state-aware constraints that depend on local marginals and measurement geometry, with natural specializations to canonical scenarios. The resulting criteria are built from first moments and standard projective measurements and provide a way to certify compatibility with local hidden variable explanations for the LPO-processed data in regimes where conventional Bell violations may be inconclusive.

Figures (4)

• Figure 1: The witness values $\Tr(\mathcal{B}\rho)$ for various inequalities --- $I_{3322}$, $S_{\hbox{CHSH}}$, and $S_{\hbox{CHSH}}^{\hbox{LPO}}$ plotted against changing $p$ values of Werner ($\rho_{\text{w}}$) state as in Eq. \ref{['eq:werner_state']}. Since $S_{\hbox{CHSH}}^{\hbox{LPO}}$ is constant and zero, it coincides with the $x$-axis. The horizontal and vertical lines of each color denote the local bounds and the corresponding $p$ values for the corresponding inequalities, respectively.
• Figure 2: Value of various Bell-type inequalities for the $\ket{\text{CG}}$ (Eq. \ref{['eq:CG_state']}). The inequalities are normalized as per Eq. \ref{['eq:chsh_coeffs']}. The particular values of $\tilde{I}_{\text{CHSH, B}}$ are not optimized, and computed under standard Bell measurement setting Eq. \ref{['eq:bell_measurement']}. The inequality values labeled by $\tilde{I}^{\text{LPO}}_{\text{CHSH, B}}$ are also computed using the same settings. The black dotted curves denote inequalities computed using the settings that maximize the $S_{\hbox{CHSH}}$. In the inset, we have zoomed in section that corroborates the results of Ref. collins_2004_relevant and act as benchmark to our computation.
• Figure 3: The normalized inequality values for the classical state given by Eq. \ref{['eq:classical']}. The plot shows that LPOW is sensitive to the internal structure of the state. Not only for pure states, but also for other superpositions it shows how the effect of phase deviates the state from pure-state behavior.
• Figure 4: The normalized witness values for the states with transition as in Eq. \ref{['eq:transition_state']}. The vertical dashed lines show the transition points for CHSH and 3322 witnesses in red and green respectively (with the corresponding $p_c$ value mentioned). The solid black line represents how LPOW changes for $p$.

Theorems & Definitions (15)

• Lemma 1
• proof
• Theorem 1
• proof
• Corollary 1
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4