arXiv subjects

Nripendra Majumdar

Publications and source records attributed to Nripendra Majumdar.

2 recordsLinked to original sources

arXiv2026

Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications

The foundational work by Bell led to an interest in understanding non-local correlations that arise from entangled states shared between distinct, spacelike-separated parties, which formed a foundation for the theory of quantum information processing. We investigate the question of maximal correlations analogous to the maximally entangled states defined in the entanglement theory of multipartite systems. In this work, we define the maximality of nonlocal correlation as being analogous to the absolutely maximally entangled state. To formalize this, we employ the sheaf-theoretic framework for contextuality, which generalizes non-locality. This provides a metric for correlations called contextual fraction (CF), which ranges from $0$ (non-contextual) to $1$ (maximally contextual). Using this, we have defined the absolutely maximal contextual correlations (AMCC), which are maximally contextual and have maximal marginals. The Popescu-Rohrlich (PR) box serves as the bipartite example, and we construct various extensions of such correlations in the tripartite case. An infinite family of various forms of AMCC is constructed using the parity check and the constraint satisfiability problem (CSP) construction. We also demonstrate the existence of maximally contextual correlations, which do not exhibit maximal marginals, and refer to them as non-AMCC. Furthermore, we showed that GHZ correlations in the $(n,2,2)$ setting give rise to AMCCs for the particular choice of measurement settings. The results are further applied to secret sharing and randomness extraction using AMCCs.

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arXiv2026

Four Party Absolutely Maximal Contextual Correlations

The Kochen Specker theorem revealed contextuality as a fundamental nonclassical feature of nature. Nonlocality arises as a special case of contextuality, where entangled states shared by space like separated parties exhibit nonlocal correlations. The notion of maximality in correlations, analogous to maximal entanglement, is less explored in multipartite systems. In our work, we have defined maximal correlations in terms of contextual models, which are analogous to absolutely maximally entangled (AME) states. Employing the sheaf theoretic framework, we introduce maximal contextual correlations associated with the corresponding maximal contextual model. The formalism introduces the contextual fraction CF as a measure of contextuality, taking values from 0 (noncontextual) to 1 (fully contextual). This enables the formulation of a new class of correlations termed absolutely maximal contextual correlations (AMCC), which are both maximally contextual and maximal marginals. In the bipartite setting, the canonical example is the Popescu Rohrlich (PR) box, while in the tripartite case, it includes Greenberger Horne Zeilinger (GHZ) correlations and three way nonlocal correlations. In this work, we extend these findings to four party correlations. Notably, no AME state exists for four qubits, which introduces a subtle difference between AMCC and AME. The construction follows the constraint satisfaction problem (CSP) and parity check methods. In particular, the explicit realization of a non AMCC correlation that is maximally contextual yet not maximal marginal is obtained within the CSP framework.

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