Entanglement of Pure States

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi +2 more

Guoying Lu

Recent research progress on quantifying and classifying entanglement for a given multipartite pure state is summarized.A new measure for the entanglement is defined,which can be used to distinguish entanglement properties pure states from one another,and quantify the measure of the entanglement for multipartite pure states.

Jessica A. Thomas

Mu-En Liu, Kai-Siang Chen, Chung-Yun Hsieh +2 more

Abstract Generic bipartite pure states of sufficiently large dimensions are overwhelmingly likely to be highly entangled. 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. Moreover, even without assuming that the global state is pure, a small number of overlapping entangled marginals of generic pure states—as we show in this work—must induce entanglement in other marginals when some mild dimension constraints are satisfied, i.e. entanglement transitivity is a generic feature of various many-body pure states. Numerically, we further observe that the genericity of (1) entangled marginals, (2) unique global compatibility, and (3) entanglement transitivity may also hold beyond the analytically established dimension constraints. We also discuss potential applications of these features of generic pure states in quantum information processing.

Subhasish Bag, Sarkar, Ramita, Prasanta Kumar Panigrahi

We propose a straightforward method to determine the maximal entanglement of pure states using the criterion of maximal I-concurrence, a measure of entanglement. The square of concurrence for a bipartition $X|X^\prime$ of a pure state is defined as $E^2_{X| X ^\prime}=2[1-tr({ρ_X}^2)]$. From this, we can infer that the concurrence $E_{X| X ^\prime}$ reaches its maximum when $tr({ρ_X}^2)$ is minimized. Using this approach, we identify numerous Absolutely Maximally Entangled (AME) pure states that exhibit maximal entanglement across all possible bipartitions. Conditions are derived for pure states to achieve maximal mixedness in all bipartitions, revealing that any pure state with an odd number of subsystem coefficients does not meet the AME criterion. Furthermore, we obtain equal maximal multipartite entangled pure states across all bipartitions using our maximal concurrence criterion.