Abstract
Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.
Highlights
Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality
In the standard quantum framework, all measurements are assumed to be local, the joint probability distributions of local measurements for a composite state shared by space-like separated parties could show nonlocal correlations
A generalization of Born rule, which gives probability of a local measurement outcome, will change nonlocality such that joint probability distributions given by generalized probability assignment could break relativistic causality
Summary
Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Bancal et al have shown theoretically that for any finite speed hypothetical influences, faster-than-light communication can be built[6] According to their results, only when the speed of the hypothetical influence is infinite, the quantum nonlocality cannot be used as a tool for faster-than-light signaling, which violates relativistic causality. Popescu and Rohrlich found that nonlocal binary devices with a certain joint probability distributions can reach the maximum upper bound 4 under no faster-than-light signaling condition, required by relativistic causality[11]. As a result, they have shown the existence of ‘superquantum’ correlations that are more nonlocal than quantum correlations under relativistic causality. No-signaling condition is not enough to determine the specific form www.nature.com/scientificreports/
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