Alladi Ramakrishnan Hall

Link representation of entanglement in quantum states

Sudipto Singha Roy

IIT--Dhanbad

: In this talk, I will present the “link representation formalism” of entanglement that we
introduced in our recent works, where we assume that entanglement entropy of any bipartition of a
quantum state can be approximated as the sum of certain link strengths connecting internal and
external sites. I will then discuss how this representation is important in quantum information,
quantum computation, and quantum many-body systems. Next, I will present examples where the
representation is exact, and then discuss several non-exact cases where we can apply certain
approximation techniques that include tensor network states, and free and interacting modes. We
will also show how the definition naturally leads to an entanglement contour of the system. Finally,
we show that the representation helps us in extending the quasi-particle picture, useful in explaining
the growth of entanglement entropy of long-range initial states when quenched under a critical
Hamiltonian. I will end the discussion with a brief summary of the extension works we are currently
doing in this direction.
References:
[1] S.Singha Roy, S. N. Santalla, J. Rodríguez-Laguna, and G. Sierra, “Entanglement as geometry and flow”,
Physical Review B 101, 195134 (2020).
[2] S. Singha Roy, S. N.Santalla, G. Sierra, and J. Rodríguez-Laguna, “Link representation of the
entanglement entropies for all bipartitions”, Journal of Physics A: Mathematical and Theoretical 54, 305301
(2021).
[3] S. Singha Roy, G. Ramírez, S. N. Santalla, G. Sierra, and J.r Rodríguez-Laguna, “Exotic correlation
spread in free-fermionic states with initial patterns”, Physical Review B 105, 214306 (2022).
[4] S. N. Santalla, G. Ramírez, S. Singha Roy, G. Sierra, and J. Rodríguez-Laguna, “Entanglement links and
the quasiparticle picture”, Physical Review B (Letter) 107, L121114 (2023).