Simulating extremal temporal correlations

Abstract

The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We discuss the resources needed to simulate the extreme points of the AoT polytope, where resources are quantified in terms of the minimal dimension, or "internal memory" of the physical system. First, we analyze the equivalence classes of the extreme points under symmetries. Second, we characterize the minimal dimension necessary to obtain a given extreme point of the AoT polytope, including a lower scaling bound in the asymptotic limit of long sequences. Finally, we present a general method to derive dimension-sensitive temporal inequalities for longer sequences, based on inequalities for shorter ones, and investigate their robustness to imperfections.

20 pages (including appendix), 8 figures

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Cited by in corpus (12)

• Kochen-Specker Contextuality
• Quantifying Quantumness of Channels Without Entanglement
• Leggett-Garg Macrorealism and temporal correlations
• Temporal correlations in the simplest measurement sequences
• Ticking-clock performance enhanced by nonclassical temporal correlations
• Structure of dimension-bounded temporal correlations
• Quantum chicken-egg dilemmas: Delayed-choice causal order and the reality of causal non-separability
• Connecting XOR and XOR* games
• Entanglement-breaking channels are a quantum memory resource
• Optimisation of time-ordered processes in the finite and asymptotic regime
• Witnessing environment dimension through temporal correlations
• Signaling between time steps does not allow for nonlocality beyond hidden nonlocality