Multipartite Causal Correlations: Polytopes and Inequalities

Abstract

We consider the most general correlations that can be obtained by a group of parties whose causal relations are well-defined, although possibly probabilistic and dependent on past parties' operations. We show that, for any fixed number of parties and inputs and outputs for each party, the set of such correlations forms a convex polytope, whose vertices correspond to deterministic strategies, and whose (nontrivial) facets define so-called causal inequalities. We completely characterize the simplest tripartite polytope in terms of its facet inequalities, propose generalizations of some inequalities to scenarios with more parties, and show that our tripartite inequalities can be violated within the process matrix formalism, where quantum mechanics is locally valid but no global causal structure is assumed.

14 pages and 1 supplementary CDF file

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Cited by in corpus (47)

• Kochen-Specker Contextuality
• Bell's Theorem for Temporal Order
• Communicating via ignorance: Increasing communication capacity via superposition of order
• Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
• Quantum circuits with classical versus quantum control of causal order
• A purification postulate for quantum mechanics with indefinite causal order
• Cyclic Quantum Causal Models
• Updating the Born rule
• Quantum computation with indefinite causal structures
• On the definition and characterisation of multipartite causal (non)separability
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Dynamics of quantum causal structures
• Connecting processes with indefinite causal order and multi-time quantum states
• Structure of temporal correlations of a qubit
• Causal order as a resource for quantum communication
• Observer-dependent locality of quantum events
• Leggett-Garg Macrorealism and temporal correlations
• Memory cost of temporal correlations
• Genuine temporal correlations can certify the quantum dimension
• The entropic approach to causal correlations
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Reversible time travel with freedom of choice
• Reversible dynamics with closed time-like curves and freedom of choice
• Unlimited non-causal correlations and their relation to non-locality
• Genuinely Multipartite Noncausality
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Simulating extremal temporal correlations
• Semi-Device-Independent Certification of Causal Nonseparability with Trusted Quantum Inputs
• Classical communication through quantum causal structures
• Composition rules for quantum processes: a no-go theorem
• Quantum enhancement to information acquisition speed
• Structure of dimension-bounded temporal correlations
• Equivalence of Grandfather and Information Antinomy Under Intervention
• Admissible Causal Structures and Correlations
• The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
• The Multi-round Process Matrix
• Trading causal order for locality
• Exploring the limits of no backward in time signalling
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• Quantum theory cannot violate a causal inequality
• Background Independence and Quantum Causal Structure
• Tripartite non-classical correlations without backwards in time signalling
• Flow of dynamical causal structures with an application to correlations
• Causal influence versus signalling for interacting quantum channels
• Telefilters, telemirrors, and causality
• Knot invariants and indefinite causal order