A Modular Operator Approach to Entanglement of Causally Closed Regions
arXiv:2201.01898 · doi:10.1007/s10773-022-05211-w
Abstract
Quantum entanglement is shown for causally separated regions along the radial direction by using a conformal quantum mechanical correspondence with conformal radial Killing fields of causal diamonds in Minkowski space. In particular, the theory of local von Neumann algebras and Tomita Takesaki modular operators is applied in the entanglement structure of causal diamonds in conformal quantum mechanics. The entanglement of local states in their respective causal regions is shown through the measures of concurrence and entanglement entropy using the Tomita Takesaki modular conjugation operator. A holographic entropy formula is derived for the conformal quantum mechanics causal diamond correspondence. A new connection is made between the thermal time flow defined by the modular group of automorphisms to the physical time flow in a causal diamond via the aforementioned correspondence. The thermal interpretation of these results via two-point thermal Green's functions and modular group flow supports the idea of a possible emergent theory of spacetime.
arXiv comment27 pages, 1 figure. Typos corrected. References added. Additional statements have been added for clarification
References in corpus (18)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Notes on Some Entanglement Properties of Quantum Field Theory
- Logarithmic Corrections to Black Hole Entropy from the Cardy Formula
- Entanglement Equilibrium and the Einstein Equation
- Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories
- Quantum fields in curved spacetime
- Conformal quantum mechanics as the CFT dual to AdS
- Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
- Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis
- Gravitational Thermodynamics of Causal Diamonds in (A)dS
- Constraining Quantum Fields using Modular Theory
- Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics
- Time as a quantum observable
- Conformal mapping of Unruh temperature
- Conformal quantum mechanics of causal diamonds
- Time Quantization and q-Deformations
- Conformal quantum mechanics and holography in noncommutative space-time
- Modular Operators and Entanglement in Supersymmetric Quantum Mechanics