PIRSA:25020053

Generic uniqueness, marginal entanglement, and entanglement transitivity

Liu, M. (2025). Generic uniqueness, marginal entanglement, and entanglement transitivity. Perimeter Institute. https://pirsa.org/25020053

Liu, Mu-En. Generic uniqueness, marginal entanglement, and entanglement transitivity. Perimeter Institute, Feb. 27, 2025, https://pirsa.org/25020053 

          @misc{ pirsa_PIRSA:25020053,
            doi = {10.48660/25020053},
            url = {https://pirsa.org/25020053},
            author = {Liu, Mu-En},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Generic uniqueness, marginal entanglement, and entanglement transitivity},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {feb},
            note = {PIRSA:25020053 see, \url{https://pirsa.org}}
          }

Mu-En Liu

Talk number
PIRSA:25020053
Collection
Talk Type
Subject
Abstract

The quantum marginal problem concerns the compatibility of given reduced states. In contrast, the entanglement transitivity problem takes compatible entangled marginals as input and ask if one can infer therefrom the entanglement of some other marginals. When this is possible, the input marginals are said to exhibit entanglement transitivity. Previous studies [Npj Quantum Inf 8, 98 (2022)] have demonstrated that certain families of states show entanglement transitivity. In this talk, we will show that when specific dimension constraints are satisfied, entanglement transitivity is possible and even generic among the marginals of pure state. To this end, we use the fact that given these constraints, the marginals of generic pure states (1) uniquely determine the global state and (2) are entangled. For the latter, our results generalize that of Aubrun et al. [Comm. Pure. Appl. Math. 67, 129 (2013)], which allows us to conclude further that sufficiently large parts of a generic multipartite pure state are entangled for any bipartition.