Correlation Measure Equivalence in Dynamic Causal Structures of Quantum Gravity

Abstract

We prove an equivalence transformation between the correlation measure functions of the causally-unbiased quantum gravity space and the causally-biased standard space. The theory of quantum gravity fuses the dynamic (nonfixed) causal structure of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity space, the events are causally nonseparable and all time bias vanishes, which makes it no possible to use the standard causally-biased entropy and the correlation measure functions. Since a corrected causally-unbiased entropy function leads to an undefined, obscure mathematical structure, in our approach the correction is made in the data representation of the causally-unbiased space. Here we prove that the standard causally-biased entropy function with a data correction can be used to identify correlations in dynamic causal structures. As a corollary, all mathematical properties of the causally-biased correlation measure functions are preserved in the causally-unbiased space. The equivalence transformation allows us to measure correlations in a quantum gravity space with the stable, well-defined mathematical background and apparatus of the causally-biased functions of quantum Shannon theory.

References in corpus (23)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Towards a derivation of holographic entanglement entropy
• General Benchmarks for Quantum Repeaters
• Quantum Computational Supremacy
• Creating and probing macroscoping entanglement with light
• End-to-end capacities of a quantum communication network
• Experimental Verification of an Indefinite Causal Order
• 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
• Closed timelike curves via post-selection: theory and experimental demonstration
• Theory of channel simulation and bounds for private communication
• General bounds for sender-receiver capacities in multipoint quantum communications
• Quantum Algorithms for Fixed Qubit Architectures
• Bounds for multi-end communication over quantum networks
• Quantum Gravity, or The Art of Building Spacetime
• Capacities of repeater-assisted quantum communications
• Entanglement, non-Markovianity, and causal non-separability
• Traversable Wormholes as Quantum Channels: Exploring CFT Entanglement Structure and Channel Capacity in Holography
• Space-time and special relativity from causal networks
• Formalism Locality in Quantum Theory and Quantum Gravity
• Quantifiable simulation of quantum computation beyond stochastic ensemble computation
• Smooth Entropy Transfer of Quantum Gravity Information Processing

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• Quantum Coherence Bounds the Distributed Discords