Within the framework of holographic duality, conditional mutual information (CMI) is often understood as a correlation between ``region pairs'' and is closely related to the concept of partial entanglement entropy (PEE). The main theme of this paper is to try to understand the rigorous physical meaning of such a region-pair correlation. This relies on the idea of holographic bit threads and the recently developed thread-state correspondence. In a sense, this effort also prompted us to give a definition of PEE based on the density matrices of the holographic distilled states. Specifically, drawing from experience with the locking multiflow configuration, we first provide a bipartite entanglement explanation for the $\mathrm{PEE}=\mathrm{CMI}$ scheme, but it leads to difficulties in characterizing the entanglement entropy of disconnected regions. We then introduce multipartite entanglement through the generalized $n$ -thread/perfect tensor state correspondence to solve this problem and explain the coincidence between CMI and tripartite information in the holographic quantum systems.Within the framework of holographic duality, conditional mutual information (CMI) is often understood as a correlation between ``region pairs'' and is closely related to the concept of partial entanglement entropy (PEE). The main theme of this paper is to try to understand the rigorous physical meaning of such a region-pair correlation. This relies on the idea of holographic bit threads and the recently developed thread-state correspondence. In a sense, this effort also prompted us to give a definition of PEE based on the density matrices of the holographic distilled states. Specifically, drawing from experience with the locking multiflow configuration, we first provide a bipartite entanglement explanation for the $\mathrm{PEE}=\mathrm{CMI}$ scheme, but it leads to difficulties in characterizing the entanglement entropy of disconnected regions. We then introduce multipartite entanglement through the generalized $n$-thread/perfect tensor state correspondence to solve this problem and explain the coincidence between CMI and tripartite information in the holographic quantum systems.

Physical review. D/Physical review. D.Nov 13, 202313 citations

Holographic Entanglement Entropy

Mukund Rangamani, Tadashi Takayanagi

Lecture notes in physicsJan 1, 2017187 citations

Distilled density matrices of holographic PEE from thread-state correspondence

Yi-Yu Lin

Within the framework of holographic duality, CMI (conditional mutual information) is often understood as a correlation between ``region pairs" and is closely related to the concept of partial entanglement entropy (PEE). The main theme of this paper is to try to understand the rigorous physical meaning of such a region-pair correlation. This relies on the idea of holographic bit threads and the recently developed thread-state correspondence. In a sense, this effort also prompted us to give a definition of PEE based on the density matrices of the holographic distilled states. Specifically, drawing from experience with the locking multiflow configuration, we first provide a bipartite entanglement explanation for the PEE=CMI scheme, but it leads to difficulties in characterizing the entanglement entropy of disconnected regions. We then introduce multipartite entanglement through the generalized $n$ -thread/perfect tensor state correspondence to solve this problem and explain the coincidence between CMI and tripartite information in the holographic quantum systems.Within the framework of holographic duality, CMI (conditional mutual information) is often understood as a correlation between ``region pairs" and is closely related to the concept of partial entanglement entropy (PEE). The main theme of this paper is to try to understand the rigorous physical meaning of such a region-pair correlation. This relies on the idea of holographic bit threads and the recently developed thread-state correspondence. In a sense, this effort also prompted us to give a definition of PEE based on the density matrices of the holographic distilled states. Specifically, drawing from experience with the locking multiflow configuration, we first provide a bipartite entanglement explanation for the PEE=CMI scheme, but it leads to difficulties in characterizing the entanglement entropy of disconnected regions. We then introduce multipartite entanglement through the generalized $n$-thread/perfect tensor state correspondence to solve this problem and explain the coincidence between CMI and tripartite information in the holographic quantum systems.

arXiv:2305.02895May 4, 20231 citation

Remarks on the entanglement entropy for disconnected regions

Horacio Casini, Marina Huerta

Few facts are known about the entanglement entropy for disconnected regions in quantum field theory. We study here the property of extensivity of the mutual information, which holds for free massless fermions in two dimensions. We uncover the structure of the entropy function in the extensive case, and find an interesting connection with the renormalization group irreversibility. The solution is a function on space-time regions which complies with all the known requirements a relativistic entropy function has to satisfy. We show that the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields in dimensions greater than two, and the massive free fields in two dimensions all fail to be exactly extensive, disproving recent conjectures. 1Few facts are known about the entanglement entropy for disconnected regions in quantum field theory. We study here the property of extensivity of the mutual information, which holds for free massless fermions in two dimensions. We uncover the structure of the entropy function in the extensive case, and find an interesting connection with the renormalization group irreversibility. The solution is a function on space-time regions which complies with all the known requirements a relativistic entropy function has to satisfy. We show that the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields in dimensions greater than two, and the massive free fields in two dimensions all fail to be exactly extensive, disproving recent conjectures. 1

Nov 26, 2012121 citations

\mathrm{PEE}=\mathrm{CMI}

scheme, but it leads to difficulties in characterizing the entanglement entropy of disconnected regions. We then introduce multipartite entanglement through the generalized

n

-thread/perfect tensor state correspondence to solve this problem and explain the coincidence between CMI and tripartite information in the holographic quantum systems.

n

-thread/perfect tensor state correspondence to solve this problem and explain the coincidence between CMI and tripartite information in the holographic quantum systems.