Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality

Abstract

The notions of causality adopted within the quantum information and spacetime physics communities are distinct. Although both notions play a role in physical experiments, their general interplay is little understood in theory. We develop a theoretical framework that connects the two causality notions, while also clearly distinguishing them. The framework describes a composition of quantum operations through feedback loops, and the embedding of the resulting, possibly cyclic information-theoretic structure in an acyclic spacetime structure. Relativistic causality (which forbids superluminal communication) follows as a graph-theoretic compatibility condition between the two structures. Formulating indefinite causal order (ICO) processes in our framework, we shed light on the links between indefinite and cyclic causality, and on questions regarding their physicality. In particular, there are several experiments that claim to implement ICO processes in Minkowski spacetime, presenting an apparent paradox: how can an indefinite information-theoretic causal structure be consistent with a definite spacetime causal structure? We address this through no-go theorems, showing that as a consequence of relativistic causality, (a) realisations of ICO processes necessarily involve the non-localisation of systems in spacetime and (b) will nevertheless admit an explanation in terms of a definite and acyclic causal order process, at a fine-grained level. This fully resolves the apparent paradox and bears implications for the physical interpretation of ICO experiments, and is achieved by introducing the concept of fine-graining that allows causal structures to be analysed at different levels of detail. Our work also sheds light on the limits of quantum information processing in spacetime and on the operational meaning of indefinite causality, within and beyond the context of a fixed spacetime.

37+30 pages, 17 figures. v4 is closest to published version. An extra result (Theorem 5.8) included in v2 but not in v1 was found to be partly incorrect, it has been removed and does not impact the main results/conclusions. v4 also includes significant improvements to the framework since v1, in terms of clarity and generality, as well as an additional result about the link to causal boxes

References in corpus (68)

• Cool horizons for entangled black holes
• Building up spacetime with quantum entanglement
• A Spin Entanglement Witness for Quantum Gravity
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Quantum correlations with no causal order
• Informational derivation of Quantum Theory
• Quantum computations without definite causal structure
• Theoretical framework for quantum networks
• Probabilistic theories with purification
• The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
• Experimental Superposition of Orders of Quantum Gates
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
• Experimental Verification of an Indefinite Causal Order
• Quantum causal modelling
• Perfect discrimination of no-signalling channels via quantum superposition of causal structures
• Indefinite Causal Order in a Quantum Switch
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
• Quantum common causes and quantum causal models
• Witnessing causal nonseparability
• The Trinity of Relational Quantum Dynamics
• Closed timelike curves via post-selection: theory and experimental demonstration
• Theory-independent limits on correlations from generalised Bayesian networks
• Quantum Graphical Models and Belief Propagation
• Quantum Metrology with Indefinite Causal Order
• Inferring causal structure: a quantum advantage
• Causal and causally separable processes
• Experimental transmission of quantum information using a superposition of causal orders
• Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity
• Bell's Theorem for Temporal Order
• Quantum Refrigeration with Indefinite Causal Order
• Quantum circuits cannot control unknown operations
• Indefinite causal order enables perfect quantum communication with zero capacity channels
• Quantum Shannon theory with superpositions of trajectories
• Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
• The quantum mechanics of time travel through post-selected teleportation
• Holographic tensor network models and quantum error correction: A topical review
• Experimental Quantum Communication Enhancement by Superposing Trajectories
• Quantum Dynamics as an analog of Conditional Probability
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• Foundations of Structural Causal Models with Cycles and Latent Variables
• Computational advantage from quantum superposition of multiple temporal orders of photonic gates
• 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
• Quantum circuits with classical versus quantum control of causal order
• A graph-separation theorem for quantum causal models
• The space of logically consistent classical processes without causal order
• Cyclic Quantum Causal Models
• Quantum computation with indefinite causal structures
• Thermodynamic advancement in the causally inseparable occurrence of thermal maps
• Experiments on quantum causality
• Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders
• Replacing the Notion of Spacetime Distance by the Notion of Correlation
• Causal structure in the presence of sectorial constraints, with application to the quantum switch
• Noncausal Page-Wootters circuits
• Composable security in relativistic quantum cryptography
• Quantum superpositions of "common-cause" and "direct-cause" causal structures
• Reversible dynamics with closed time-like curves and freedom of choice
• Causal and compositional structure of unitary transformations
• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
• Indefinite Causal Orders from Superpositions in Time
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Fundamental limits for realising quantum processes in spacetime
• Gravitational quantum switch on a superposition of spherical shells
• Causal influence in operational probabilistic theories
• The Multi-round Process Matrix

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