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.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.

arXiv:2505.20420Quantum Science and TechnologyDec 23, 20252 citations

Quantum Entanglement in High Dimensions

Guillaume Aubrun

Lecture notes in mathematicsJan 1, 20170 citations

Entanglement of Pure States

Stig Stenholm

Foundations of PhysicsJan 26, 20090 citations

Bounds on negativity of superpositions

Yong-Cheng Ou, Heng Fan

For pure bipartite superposed states, the entanglement quantified by negativity is studied. If the entanglement is quantified by concurrence, we show that two pure states with high fidelity to one another have nearly the same entanglement. We deduce an inequality in which the concurrence is known to be a continuous function in infinite dimensions. The main result of this paper is to give the bounds on the negativity of a bipartite state in terms of the entanglement of the states being superposed. These bounds may be used in estimating the entanglement of a given state.For pure bipartite superposed states, the entanglement quantified by negativity is studied. If the entanglement is quantified by concurrence, we show that two pure states with high fidelity to one another have nearly the same entanglement. We deduce an inequality in which the concurrence is known to be a continuous function in infinite dimensions. The main result of this paper is to give the bounds on the negativity of a bipartite state in terms of the entanglement of the states being superposed. These bounds may be used in estimating the entanglement of a given state.

arXiv:0704.0757Physical Review AAug 22, 200742 citations

Advances in high-dimensional quantum entanglement

Manuel Erhard, Mario Krenn, Anton Zeilinger

arXiv:1911.10006Nature Reviews PhysicsJun 25, 2020650 citations

Bounds on entanglement in qudit subsystems

Viv M. Kendon, Karol Życzkowski, William J. Munro

The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterized by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other $N\ensuremath{-}m$ qudits. We examine the entanglement in the space of mixed states of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than $N/3$ qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than $N/3$ falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterized by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other $N\ensuremath{-}m$ qudits. We examine the entanglement in the space of mixed states of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than $N/3$ qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than $N/3$ falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.

arXiv:quant-ph/0203037Physical Review ADec 12, 200253 citations

N/3

qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than

N/3

falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.