The product structure of MPS-under-permutations

Autor(en)

Marta Florido-Llinàs, Álvaro M. Alhambra, Rahul Trivedi, Norbert Schuch, David Pérez-García, J. Ignacio Cirac

Abstrakt

Tensor network methods have proved to be highly effective in addressing a wide variety of physical scenarios, including those lacking an intrinsic one-dimensional geometry. In such contexts, it is possible for the problem to exhibit a weak form of permutational symmetry, in the sense that entanglement behaves similarly across any arbitrary bipartition. In this paper, we show that translationally-invariant (TI) matrix product states (MPS) with this property are trivial, meaning that they are either product states or superpositions of a few of them. The results also apply to non-TI generic MPS, as well as further relevant examples of MPS including the W state and the Dicke states in an approximate sense. Our findings motivate the usage of ans\"atze simpler than tensor networks in systems whose structure is invariant under permutations.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation, Institut für Mathematik

Externe Organisation(en)

Max-Planck-Institut für Quantenoptik, Munich Center for Quantum Science and Technology (MCQST), Instituto de Física Teórica UAM-CSIC, Universidad Complutense De Madrid

Seiten

1-15

DOI

https://doi.org/10.48550/arXiv.2410.19541

Publikationsdatum

10-2024

ÖFOS 2012

103025 Quantenmechanik, 103036 Theoretische Physik, 101028 Mathematische Modellierung

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/61c096ab-80aa-48c3-b0e8-b7122ebd24b2