Detecting entanglement in quantum many-body systems via permutation moments

TL;DR

This paper introduces a new framework using permutation moments to detect multipartite entanglement in quantum many-body systems, overcoming limitations of traditional methods and revealing entanglement transitions.

Contribution

The authors develop a permutation moments-based framework for entanglement detection that is experimentally feasible and applicable to complex many-body quantum systems.

Findings

Effective detection of entanglement in multi-qubit Ising models

Quantification of entanglement with physical meaning

Observation of entanglement scaling transition

Abstract

Multipartite entanglement plays an essential role in both quantum information science and many-body physics. Due to the exponentially large dimension and complex geometric structure of the state space, the detection of entanglement in many-body systems is extremely challenging in reality. Conventional means, like entanglement witness and entropy criterion, either highly depend on the prior knowledge of the studied systems or the detection capability is relatively weak. In this work, we propose a framework for designing multipartite entanglement criteria based on permutation moments, which have an effective implementation with either the generalized control-SWAP quantum circuits or the random unitary techniques. These criteria show strong detection capability in the multi-qubit Ising model with a long-range $XY$ Hamiltonian. The quantities associated with these criteria have clear physical meaning and can be used as entanglement quantifiers, with which we show the entanglement scaling transition in a quantum dynamical phase transition. Furthermore, our framework can also be generalized to detect the much more complicated entanglement structure in quantum many-body systems.