Loss of exchange symmetry in multiqubit states under Ising chain evolution

TL;DR

This paper investigates how Ising chain evolution affects exchange symmetry in multiqubit states, revealing that symmetry is generally lost except for specific 4-qubit W states, highlighting limitations in symmetry preservation.

Contribution

It demonstrates that Ising chain evolution typically breaks exchange symmetry in symmetric multiqubit states, except for certain 4-qubit W states, providing new insights into symmetry dynamics.

Findings

All N-qubit symmetric states (N ≥ 5) lose symmetry after Ising evolution.

4-qubit W states uniquely retain symmetry under Ising evolution.

Exchange symmetry is generally not preserved in multiqubit Ising chain dynamics.

Abstract

Keeping in view the exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that Ising type Hamiltonian does not retain the exchange symmetry of initially symmetric multiqubit states. Specifically, we show that all N-qubit states (N greater than or equal to 5) obeying permutation symmetry lose their symmetry after evolution with one dimensional Ising chain with nearest neighbor interactions. Among 4-qubit symmetric pure states, only W type states retain their symmetry under time evolution with Ising Hamiltonian.