Paradox-free Non-Causality Achieves Equivalence to Non-Locality Without Entanglement

The fundamental nature of cause and effect faces scrutiny when considering scenarios allowing information to travel backwards in time, a concept explored through the theoretical framework of closed timelike curves. Hippolyte Dourdent, Kyrylo Simonov, and Andreas Leitherer, alongside Emanuel-Cristian Boghiu, Ravi Kunjwal, and Saronath Halder, investigate how to maintain logical consistency in such systems, avoiding paradoxes while adhering to established physical principles. Their work presents a comprehensive understanding of ‘process functions’, which describe how information behaves in these unusual circumstances, and demonstrates a surprising equivalence between non-causality, where the order of events becomes blurred, and a specific type of non-locality, a phenomenon where distant objects exhibit correlations beyond what classical physics allows, but crucially, without relying on the quantum phenomenon of entanglement. This achievement establishes a powerful connection between these concepts, offering a systematic way to build models exhibiting these properties and revealing previously hidden relationships between fundamental inequalities governing information transfer.

Quantum States and Consistent Time Travel

This work investigates the implications of restricting quantum operations to those that are completely positive trace-preserving (CPTP) maps when considering closed timelike curves, theoretical paths allowing information to return to its own past. The research team explores conditions under which CPTP maps can consistently evolve quantum states along these curves, establishing a framework for self-consistent quantum mechanics in the presence of time travel. Researchers demonstrate that the set of consistent CPTP maps is restricted, and not all maps can evolve states along CTCs without inconsistencies, deriving a necessary and sufficient condition for consistency based on the map’s completely positive extension. The study also establishes a connection between map consistency and spacetime geometry, revealing that certain configurations may preclude self-consistent quantum mechanics, and shows that the allowed set of maps shrinks as the complexity of the time loop increases.

Tripartite Validity From Output-Reduced Functions

This research examines the relationship between the validity of a complex function taking three inputs and the validity of simpler functions derived from it. The team investigates whether valid output-reduced functions, obtained by treating one input as a parameter, guarantee the validity of the original function, focusing on functions that are one-way non-signaling and satisfy a fixed-point condition. The analysis considers various cases based on the constancy of function components, revealing a trade-off that can ensure overall validity, but also identifying a problematic “global loop” function that demonstrates the condition is not always sufficient, meaning valid output-reduced functions do not always guarantee a valid tripartite function.

Non-Causality Equivalence to Quantum Nonlocality Without Entanglement

Scientists have fully characterized process functions, deterministic classical communication structures that allow correlations defying conventional causal order, yet remain logically consistent. This work establishes a fundamental equivalence between these process functions and unambiguous complete product bases, sets of states where each local measurement yields a unique result, demonstrating that non-causality within process functions directly corresponds to quantum nonlocality without entanglement for these bases. The team generalized previous findings to systems with arbitrary local dimensions and any number of interacting parties, enabling the systematic construction of both non-causal process functions and unambiguous bases, and revealing a connection between non-signaling and causal inequalities.

Non-Causality, Process Functions, and Unambiguous Bases

This research establishes a connection between scenarios allowing influences outside of standard causal order and the properties of mathematical structures called process functions. Scientists have achieved the first complete characterization of these process functions, demonstrating how they can be systematically defined and constructed, even in complex systems. The team reveals that non-causal process functions are linked to unambiguous complete product bases, implying that the ability to send signals backwards in time mirrors a specific type of nonlocality, while acknowledging that some ambiguous bases require multi-round communication for measurement and warrant further investigation.