Evolution and Symmetry of Multipartite Entanglement

TL;DR

This paper introduces a simple law describing how multipartite entanglement evolves under physical processes, showing it depends on a single entanglement resilient factor and parallels bipartite entanglement behavior.

Contribution

It presents a universal factorization law for multipartite entanglement decay, extending previous bipartite results and introducing the concept of entanglement asymmetry under permutations.

Findings

Multipartite entanglement decay is governed by a single entanglement resilient factor.

The law reduces to known bipartite results for two qubits.

Conditions for permutation-based entanglement transformations are identified.

Abstract

We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilient factor (ERF). Since the ERF is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of Nature Physics 4, 99 (2008). In addition, for a permutation $P$, we provide an operational definition of $P$-asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.