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It closely resembles the more well-known quantum information teleportation (QIT) where quantum information can be sent through an entangled pair with LOCC. It is tempting to ask how QET is related to QIT. Here we report a first study of this connection. Despite the apparent similarity, we show that these two phenomena are not only distinct but moreover are mutually competitive. We show a perturbative trade-off relation between their performance in a thermal entangled chaotic many-body system, in which both QET and QIT are simultaneously implemented through a traversable wormhole in an emergent spacetime. Motivated by this example, we study a generic setup of two entangled qudits and prove a universal non-perturbative trade-off bound. It shows that for any teleportation protocol, the overall performance of QET and QIT together is constrained by the entanglement resource. We discuss some explanations of our results.<\/jats:p>","DOI":"10.22331\/q-2024-12-12-1564","type":"journal-article","created":{"date-parts":[[2024,12,12]],"date-time":"2024-12-12T13:12:02Z","timestamp":1734009122000},"page":"1564","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Quantum Energy Teleportation versus Information Teleportation"],"prefix":"10.22331","volume":"8","author":[{"given":"Jinzhao","family":"Wang","sequence":"first","affiliation":[{"name":"Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305"}]},{"given":"Shunyu","family":"Yao","sequence":"additional","affiliation":[{"name":"Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305"}]}],"member":"9598","published-online":{"date-parts":[[2024,12,12]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Charles H Bennett, Gilles Brassard, Claude Cr\u00e9peau, Richard Jozsa, Asher Peres, and William K Wootters. 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