Bounding quantum correlations with indefinite causal order

Abstract

Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the past or space-like separated from any other operation. Recently, a framework was developed where quantum theory is assumed to be valid in local laboratories, but where no reference is made to any global causal relations between the operations in the laboratories. The framework was shown to allow for correlations that violate a bipartite causal inequality. Here we prove that the maximal violation of the causal inequality is upper bounded (analogously to the "Tsirelson bound") under a restricted set of local operations involving traceless binary observables. The bound is lower than what is algebraically possible.

6 pages, 2 figures, close to the published version

References in corpus (3)

• Computational advantage from quantum-controlled ordering of gates
• Simple explanation of the quantum violation of a fundamental inequality
• Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios

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• Causal and causally separable processes
• The simplest causal inequalities and their violation
• A purification postulate for quantum mechanics with indefinite causal order
• Optimal quantum networks and one-shot entropies
• The space of logically consistent classical processes without causal order
• Operational quantum theory without predefined time
• Witnesses of causal nonseparability: an introduction and a few case studies
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Entanglement, non-Markovianity, and causal non-separability
• How device-independent approaches change the meaning of physical theory
• Reconstructing quantum theory from diagrammatic postulates
• Causal Boxes: Quantum Information-Processing Systems Closed under Composition
• Causality re-established
• Causally nonseparable processes admitting a causal model
• Noncausal Page-Wootters circuits
• Device-independent test of causal order and relations to fixed-points
• Entanglement Entropy of Free Fermions in Timelike Slices
• Quantum Causal Influence
• Tsirelson bounds for quantum correlations with indefinite causal order
• Consistent circuits for indefinite causal order
• Quantifying Causal Influence in Quantum Mechanics
• Biased Non-Causal Game
• Practical implementation of arbitrary nonlocal controlled-unitary gate via indefinite causal order
• No quantum advantage for violating fixed-order inequalities?