On the Contextuality of Multi-Agent Quantum Paradoxes via Anomalous Weak Values

Abstract

In this thesis we investigate the role of quantum contextuality in multi-agent paradoxes by tracing the emergence of anomalous weak values (AWVs). Starting from the logical pre- and post-selection (LPPS) formulation of the Hardy paradox, we construct an explicit one-way LOCC protocol that reproduces its statistics and provides a proof of Kochen–Specker (KS) contextuality. We then embed this construction into a particular extended Wigner’s friend argument known as Local Friendliness (LF). In a coarse-grained model where two friends perform joint two-qubit measurements, we show that the LF assumptions lead to a logical contradiction identical to that of the LPPS Hardy paradox, thereby providing a proof of the LF no-go theorem. We further develop two extensions of this model in which the intermediate measurements are implemented as weak interactions. In both cases, the anomalous weak value of –1 is preserved, confirming its robustness as a witness of contextuality in this setting. A complementary fine-grained decomposition resolves each joint measurement into our LOCC-based construction. Although the same logical contradiction is recovered under the LF assumption, the weak measurement schemes in this decomposition no longer exhibit AWVs. This reveals an apparent tension between two seemingly equivalent descriptions, suggesting that the presence of AWVs may depend sensitively on how multi-agent scenarios are modeled.