ER = EPR? Topology and Quantum Entanglement Nigel Shen1, Jonathan Bain 2 1. Research Assistant, 2. Faculty Mentor Abstract Conceptual Map Maldacena & Susskind’s “ER=EPR” Quantum Entanglement Wormhole hypothesis claims that two physical systems Entanglement Entropy Maximin Cross-Sectional Area of Throat in a quantum entangled (“EPR”, or Einstein- SA = −Tr(ρAlogρA) *Under ER=EPR, a wormhole’s maximin Used to describe the extent to which a cross-sectional area is considered the Podolsky-Rosen) state are connected by an bipartite system AB is entangled. dual of entanglement entropy. Einstein-Rosen (“ER”) wormhole. More No Superluminal Signaling Non-traversability generally, it claims that spacetime topology Quantum entanglement cannot be used to Any future-directed curve that passes is the “dual” of quantum entanglement: send superluminal signals. through a wormhole must become space- physical systems in a quantum entangled like along some of its extent. state can be described as systems Quantum Cloning [2] Topology Change connected by a wormhole, and vice-versa. If a multipartite entangled state is the result of If a wormhole has formed as a result of Future Work cloning one of the substates B of a bipartite topology change, and if it violates the null Our project’s goals are to assess the We have now created a conceptual map entangled state AB, and: energy condition, then it is traversable, between entanglement and wormholes. While motivations for “ER=EPR”, including AdS (1) all B-clones remain entangled with A; which indicates superluminal signaling. this map exposes intriguing relations that /CFT theory and the Black Hole Firewall (2) entanglements of different subsystems do not influence each other; support ER=EPR, additional questions remain. Problem, and to construct a conceptual map then it facilitates superluminal signaling. First, we need to further specify the meaning that relates characteristics of wormholes to of non-detectability, since it risks making Entanglement Non-detectability Wormhole Non-detectability characteristics of entanglement. There is no observable that represents There is no local curvature measurement ER=EPR unverifiable. Second, entanglement monogamy is potentially contradictory to Motivations for ER=EPR [1] entanglement in terms of a linear operator. that can distinguish between a one-sided black hole spacetime and a two-sided ER=EPR's resolution to the Firewall Paradox: 1. Correspondence between extended AdS- black hole (i.e., wormhole) spacetime. RB cannot be wormhole-connected with A Schwarzschild spacetime and entangled vacuum Entanglement Conservation Area Conservation since it is maximally entangled with B. Finally, state of a CFT. For a bipartite system AB, the entanglement The maximin cross-sectional area of a more conceptual work could be done on the 2. Resolves Firewall Problem. entropy SA of subsystem A is invariant under wormhole is invariant under local relation between ER=EPR and recent local operations. operations performed near its mouths. derivations of the Einstein equations from 3. No superluminal signals, and no creation and/or entanglement first principles. increase by LOCC. Entanglement Monogamy [3] Wormhole Monogamy If A and B are maximally entangled, then If a "maximal" wormhole connects regions neither A nor B is entangled with any other A and B, then neither A nor B can be Select Works Cited Firewall Paradox system C. connected by a wormhole to any other [1] Maldacena, J. & L. Susskind (2013) "Cool Horizons for Entangled region C. Black Holes", Fortschritte der Physik 61, 781. (i) B is maximally entangled with A. [2] Remmen, G., N. Bao, & J. Pollack (2015) “Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality”, (ii) B is maximally entangled with RB. Fortschritte der Physik 63, 705. (iii) B cannot be maximally entangled with two [3] Gharibyan, H. & R. Penna (2014) “Are entangled particles connected by wormholes? Evidence forthe ER 1⁄4 EPR conjecture from entropy systems. inequalities”, Physical Review D 89, 066001-1. ER=EPR Resolution Deny (i): When R is distilled, it "disrupts" A via Acknowledgement B The authors thank NYU Tandon School of Engineering’s Office of a wormhole connection. P1. An Illustration of Firewall Paradox P2. Maximin Cross Sectional Area of Throat Undergraduate Academics for generous funding of the project.