Biased Non-Causal Game
Some Sankar Bhattacharya, Manik Banik

TL;DR
This paper extends the process matrix formalism to biased causal games, deriving a biased causal inequality and demonstrating that certain inseparable process matrices can violate it, revealing new insights into quantum causality without a global order.
Contribution
It introduces a biased causal inequality and shows that inseparable process matrices can violate it for arbitrary biases, expanding understanding of non-causal quantum correlations.
Findings
Inseparable qubit process matrices can violate the biased causal inequality.
Maximal violation derived under local traceless binary observables.
Threshold bias identified beyond which violation is impossible with certain operations.
Abstract
The standard formulation of quantum theory assumes that events are ordered is a background global causal structure. Recently in Ref.[], the authors have developed a new formalism, namely, the \emph{process matrix} formalism, which is locally in agreement with quantum physics but assumes no global causal order. They have further shown that there exist \emph{non-causal} correlations originating from \emph{inseparable} process matrices that violate a \emph{causal inequality} (CI) derived under the assumption that events are ordered with respect to some global causal relation. This CI can be understood as a guessing game, where two separate parties, say Alice and Bob, generate random bits (say input bit) in their respective local laboratories. Bob generates another random bit (say…
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Taxonomy
TopicsQuantum Mechanics and Applications · Quantum Information and Cryptography · Quantum Computing Algorithms and Architecture
