Large Parts are Generically Entangled Across All Cuts

TL;DR

This paper demonstrates that large marginals of generic multipartite pure states are typically entangled across all bipartitions, highlighting their robustness and potential utility in quantum information processing.

Contribution

It establishes that sufficiently large marginals of generic multipartite states are entangled across all bipartitions and explores entanglement transitivity in many-body systems.

Findings

Large marginals are entangled across all bipartitions.

Entanglement transitivity is a generic feature in many-body systems.

Numerical evidence suggests these properties extend beyond proven dimension constraints.

Abstract

Generic high-dimensional bipartite pure states are overwhelmingly likely to be highly entangled. Remarkably, this ubiquitous phenomenon can already arise in finite-dimensional systems. However, unlike the bipartite setting, the entanglement of generic multipartite pure states, and specifically their multipartite marginals, is far less understood. Here, we show that sufficiently large marginals of generic multipartite pure states, accounting for approximately half or more of the subsystems, are entangled across all bipartitions. These pure states are thus robust to losses in entanglement distribution and potentially useful for quantum information protocols where the flexibility in the collaboration among subsets of clients is desirable. We further show that these entangled marginals are not only shareable in closed systems, but must also induce entanglement in other marginals when some mild dimension constraints are satisfied, i.e., entanglement transitivity is a generic feature of various many-body closed systems. We further observe numerically that the genericity of (1) entangled marginals, (2) unique global compatibility, and (3) entanglement transitivity may also hold beyond the analytically established dimension constraints, which may be of independent interest.