Quantum Causal Influence
arXiv:1811.05485 · doi:10.1007/JHEP07(2019)042
Abstract
We introduce a framework to study the emergence of time and causal structure in quantum many-body systems. In doing so, we consider quantum states which encode spacetime dynamics, and develop information theoretic tools to extract the causal relationships between putative spacetime subsystems. Our analysis reveals a quantum generalization of the thermodynamic arrow of time and begins to explore the roles of entanglement, scrambling and quantum error correction in the emergence of spacetime. For instance, exotic causal relationships can arise due to dynamically induced quantum error correction in spacetime: there can exist a spatial region in the past which does not causally influence any small spatial regions in the future, but yet it causally influences the union of several small spatial regions in the future. We provide examples of quantum causal influence in Hamiltonian evolution, quantum error correction codes, quantum teleportation, holographic tensor networks, the final state projection model of black holes, and many other systems. We find that the quantum causal influence provides a unifying perspective on spacetime correlations in these seemingly distinct settings. In addition, we prove a variety of general structural results and discuss the relation of quantum causal influence to spacetime quantum entropies.
arXiv comment50+18 pages, 27 figures; v2: minor fixes
References in corpus (47)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Efficient classical simulation of slightly entangled quantum computations
- A bound on chaos
- Black holes and the butterfly effect
- Black holes as mirrors: quantum information in random subsystems
- How to share a quantum secret
- Building up spacetime with quantum entanglement
- Fast Scramblers
- A class of quantum many-body states that can be efficiently simulated
- Entanglement Renormalization and Holography
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Area laws in quantum systems: mutual information and correlations
- Quantum correlations with no causal order
- Localized shocks
- Tensor renormalization group approach to 2D classical lattice models
- Holographic duality from random tensor networks
- Jerusalem Lectures on Black Holes and Quantum Information
- Towards the fast scrambling conjecture
- Random Quantum Circuits are Approximate 2-designs
- The black hole final state
- Chaos, Complexity, and Random Matrices
- Quantum causal modelling
- Quantum common causes and quantum causal models
- On entanglement spreading in chaotic systems
- Inferring causal structure: a quantum advantage
- Causal and causally separable processes
- Black Hole Entanglement and Quantum Error Correction
- Comment on "The black hole final state"
- Generalization of Quantum Error Correction via the Heisenberg Picture
- Quantum Error Correction of Observables
- A graph-separation theorem for quantum causal models
- The Operator Tensor Formulation of Quantum Theory
- Experimental Test of Nonlocal Causality
- Superdensity Operators for Spacetime Quantum Mechanics
- Almost Certain Escape from Black Holes
- Operational quantum theory without predefined time
- Operational formulation of time reversal in quantum theory
- Quantum-coherent mixtures of causal relations
- Dynamics of quantum causal structures
- Holographic coherent states from random tensor networks
- Bounding quantum correlations with indefinite causal order
- Each instant of time a new Universe
- Measurements without Probabilities in the Final State Proposal
- Process Products Need Qualification
- Quantum from principles without assuming definite causal structure
- Generalizing Entanglement
Cited by in corpus (14)
- Low-dimensional de Sitter quantum gravity
- Effective entropy of quantum fields coupled with gravity
- From time-reversal symmetry to quantum Bayes' rules
- Signaling and Scrambling with Strongly Long-Range Interactions
- Entanglement Entropy of Free Fermions in Timelike Slices
- Quantum space-time marginal problem: global causal structure from local causal information
- Uniqueness of quantum state over time function
- Exactly solvable many-body dynamics from space-time duality
- Holographic networks for (1+1)-dimensional de Sitter spacetime
- Space-time generalization of mutual information
- Causal influence in operational probabilistic theories
- Causal influence versus signalling for interacting quantum channels
- Tensor networks for quantum causal histories
- Tri-unitary quantum circuits