Optimization of entanglement generation processes via graphs

I explain a graph-based framework that provides a systematic strategy for designing optimized schemes to generate multipartite entangled states in linear quantum networks. We call the graph formalism the Linear Quantum Graph Picture (LQG picture).

This talk consists of three parts:
First, I explain the mapping dictionary and important mathematical properties of the LQG picture.
Second, I discuss its application to post-selected schemes. I also explain that many graph solutions in a recent work (PRX Quantum 5:040350 (2024) by K. Mahdavipour et al.) are reproductions of graph solutions originally introduced in Quantum:5, 611 (2021) by S. Chin et al., based on essentially the same graph mapping.
Third, I show how the LQG picture simplifies and optimizes the scheme design of heralded multipartite entangled states, with examples of various qubit entangled states (GHZ, W, N=3 Type 5 state, arbitrary caterpillar graph states) and qudit (GHZ, N-partite N-level (anti-)symmetric states).

References:

[1] Seungbeom Chin, Yong-Su Kim, and Sangmin Lee."Graph Picture of Linear Quantum Networks and Entanglement." Quantum 5:611 (2021).

[2] Seungbeom Chin, Yong-Su Kim, and Marcin Karczewski. "Shortcut to Multipartite Entanglement Generation: A Graph Approach to Boson Subtractions." npj Quantum Information 10.1:67 (2024).

[3] Seungbeom Chin, Marcin Karczewski, and Yong-Su Kim. "Heralded Optical Entanglement Generation via the Graph Picture of Linear Quantum Networks." Quantum 8:1762 (2024).

[4] Seungbeom Chin, Junghee Ryu, and Yong-Su Kim. "Exponentially enhanced scheme for the heralded qudit Greenberger-Horne-Zeilinger state in linear optics." Physical Review Letters 133:253601 (2024).