The space of logically consistent classical processes without causal order

Abstract

Classical correlations without predefined causal order arise from processes where parties manipulate random variables, and where the order of these interactions is not predefined. No assumption on the causal order of the parties is made, but the processes are restricted to be logically consistent under any choice of the parties' operations. It is known that for three parties or more, this set of processes is larger than the set of processes achievable in a predefined ordering of the parties. Here, we model all classical processes without predefined causal order geometrically and find that the set of such processes forms a polytope. Additionally, we model a smaller polytope --- the deterministic-extrema polytope --- where all extremal points represent deterministic processes. This polytope excludes probabilistic processes that must be --- quite unnaturally --- fine-tuned, because any variation of the weights in a decomposition into deterministic processes leads to a logical inconsistency.

14 pages, 12 figures, 1 table, improved, references updated

References in corpus (11)

• No extension of quantum theory can have improved predictive power
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Witnessing causal nonseparability
• Quantum Time
• Quantum superposition of the order of parties as a communication resource
• The simplest causal inequalities and their violation
• Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios
• Operational formulation of time reversal in quantum theory
• Quantum clocks and their synchronisation - the Alternate Ticks Game
• Acausal measurement-based quantum computing
• Quantum correlations and causal structures

Cited by in corpus (50)

• Quantum causal modelling
• Causal and causally separable processes
• The simplest causal inequalities and their violation
• Experimental Quantum Communication Enhancement by Superposing Trajectories
• Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
• A purification postulate for quantum mechanics with indefinite causal order
• Multipartite Causal Correlations: Polytopes and Inequalities
• Cyclic Quantum Causal Models
• Quantum computation with indefinite causal structures
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• How device-independent approaches change the meaning of physical theory
• Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
• Causal Boxes: Quantum Information-Processing Systems Closed under Composition
• Causation does not explain contextuality
• Causal structure in the presence of sectorial constraints, with application to the quantum switch
• Noncausal Page-Wootters circuits
• Device-independent test of causal order and relations to fixed-points
• The entropic approach to causal correlations
• Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH
• Evading noise in multiparameter quantum metrology with indefinite causal order
• Reversible time travel with freedom of choice
• Consequences of preserving reversibility in quantum superchannels
• Reversible dynamics with closed time-like curves and freedom of choice
• Computational tameness of classical non-causal models
• Unlimited non-causal correlations and their relation to non-locality
• Reassessing thermodynamic advantage from indefinite causal order
• Quantum Causal Models
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Non-causal computation
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
• Breaking the limits of purification: Postselection enhances heat-bath algorithmic cooling
• Quantum superposition of causal structures as a universal resource for local implementation of nonlocal quantum operations
• Equivalence of Grandfather and Information Antinomy Under Intervention
• Admissible Causal Structures and Correlations
• A no-go theorem for superpositions of causal orders
• Quantum Supermaps are Characterized by Locality
• Trading causal order for locality
• The Multi-round Process Matrix
• Tsirelson bounds for quantum correlations with indefinite causal order
• Multi-system measurements in generalized probabilistic theories and their role in information processing
• Consistent circuits for indefinite causal order
• Toward an Experimental Device-Independent Verification of Indefinite Causal Order
• Topological obstructions to quantum computation with unitary oracles
• Algebraic and geometric properties of local transformations
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• Classical and Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
• A Profunctorial Semantics for Quantum Supermaps
• No quantum advantage for violating fixed-order inequalities?