# Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes

**Authors:** Grant N. Remmen, Ning Bao, Jason Pollack  
**arXiv:** [1604.08217](https://arxiv.org/abs/1604.08217)  
**Date:** 2016-04-27  
**Summary page:** https://www.summarizepaper.com/en/paper/1604.08217v1/

## Key points

- Authors Grant N. Remmen, Ning Bao, and Jason Pollack explore entanglement conservation in the context of ER=EPR correspondence
- Quantum entanglement between a system and its complement remains preserved under unitary operations
- ER=EPR hypothesis suggests a conservation principle for wormholes based on entanglement preservation
- Novel area theorem derived from general relativity principles focuses on dynamic wormholes and black holes in spacetime with null curvature condition
- Maximin area for a subset of horizons remains invariant under classical time evolution along outermost apparent horizons
- The new area theorem provides a gravitational counterpart to entanglement conservation and characterizes ER=EPR duality in classical scenarios
- Their work contributes to understanding quantum entanglement, wormholes, and connections between physics concepts beyond theoretical frameworks

## Summary

In their paper titled "Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes," authors Grant N. Remmen, Ning Bao, and Jason Pollack explore the concept of entanglement conservation within the framework of the ER=EPR correspondence. This correspondence posits a connection between quantum entanglement and wormholes. They demonstrate how in quantum mechanics, the entanglement between a system and its complement remains preserved under unitary operations that act independently on each component. Building upon this idea, the ER=EPR hypothesis suggests a similar conservation principle for wormholes. The authors present a novel area theorem derived from general relativity principles. They focus on dynamic wormholes and black holes within a spacetime that adheres to the null curvature condition. In this setting, they establish that the maximin area for a specific subset of horizons remains invariant under classical time evolution along the outermost apparent horizons. This evolution includes horizon mergers and the introduction of classical matter satisfying the null energy condition. Through their new area theorem, which serves as the gravitational counterpart to entanglement conservation, Remmen, Bao, and Pollack offer an explicit characterization of the ER=EPR duality in classical scenarios. Their work not only contributes to our understanding of quantum entanglement and wormholes but also sheds light on profound connections between seemingly disparate concepts in physics. The implications of their findings extend beyond theoretical frameworks to potentially impact our comprehension of fundamental aspects of spacetime geometry and quantum information theory.