Does connected wedge imply distillable entanglement?

          @misc{ pirsa_PIRSA:25060011,
            doi = {10.48660/25060011},
            url = {https://pirsa.org/25060011},
            author = {Mori, Takato},
            keywords = {Quantum Gravity, Quantum Information},
            language = {en},
            title = {Does connected wedge imply distillable entanglement?},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {jun},
            note = {PIRSA:25060011 see, \url{https://pirsa.org}}
          }
          

Abstract

In holography, when two boundary subsystems have large mutual information, they are connected by their entanglement wedge. However, it remains mysterious whether these subsystems are EPR-like entangled. In this talk, I resolve this problem by finding bulk duals of one-shot distillable entanglement. Namely, I show that in one-shot scenarios: i) there is no distillable entanglement only by local operations at leading order in $G_N$, suggesting the absence of bipartite entanglement in a holographic mixed state, and ii) one-way LOCC-distillable entanglement is related to the entanglement wedge cross section, which is further dual to entanglement of formation. By demonstrating an explicit distillation protocol by holographic measurements, I conclude that a connected wedge does not necessarily imply finite distillable entanglement even when one-way LOCC is allowed. This talk is based on arXiv:2411.03426 [hep-th] and 2502.04437 [quant-ph].