## Upcoming Seminars

Date/Place | Aug. 21st (Tue.) (Informal) 15:30-16:30 / H711 |
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Name | Yuta Hamada (U. of Wisconsin, KEK) |

Title | Weak Gravity Conjecture from Unitarity |

Abstract | Weak Gravity Conjecture provides the lower bound on the Abelian gauge coupling in the theory of quantum gravity. In this talk, I will show that, under several assumptions, a class of weak gravity conjecture follows from the unitarity of the quantum field theory. |

Date/Place | Oct. 2th (Tue.) 15:30-16:30 / H711 |
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Name | Koji Umemoto (YITP) |

Title | Entanglement of Purification in Holography and its Multipartite Generalization |

Abstract |
It has been more than 10 years since a connection between quantum
information theory and quantum gravity was found in the context of AdS/
CFT correspondence. There it was conjectured that the entanglement
entropy in holographic CFTs is equal to the minimal geometrical area of
certain codimention-2 surfaces in the bulk AdS. This is now called Ryu-
Takayanagi or holographic entanglement entropy formula and has passed
substantial tests. Since the entanglement entropy represents an amount
of quantum entanglement for pure states, this formula motivate us to
investigate the potential relationship between boundary entanglement and
bulky geometry. However, one problem here is that one can not use the entanglement entropy as a measure of entanglement for mixed states: the entanglement entropy loose its meaning of “entanglement” for mixed states and becomes just a von Neumann entropy of considered subsystem. Such mixed states naturally appear in AdS/CFT e.g. when one considers bipartite subsystems on the boundary, or black hole geometry itself is also mixed. In this seminar, we talk about a generalization of the holographic entanglement entropy formula which is applicable for mixed states. We propose that the entanglement of purification, which is a generalization of entanglement entropy for mixed states capturing both quantum entanglement and classical correlations, has a gravitational counterpart expressed by a certain minimal area of codimension-2 surface in the entanglement wedge. We show that known properties of entanglement of purification are indeed satisfied by the conjectured holographic counterpart, and also give a heuristic explanation why this relation happens based on the tensor network description. On the other hand, another problem is that in multipartite systems (such as 3 qubits) we have to deal with multipartite entanglement to know the detailed structure of quantum states. Again the entanglement entropy can not be used for this purpose. Then we also generalize the holographic entanglement of purification conjecture to multipartite setups and test its validity. We define a multipartite generalization of entanglement of purification and that of holographic counterpart, and then prove their properties independently. We confirm that these two quantity indeed share all the properties we concerned. These agreements support the multipartite (including bipartite) holographic entanglement of purification conjecture. |