Year: 2026
Type: preprint
Abstract: In the presence of a globally conserved charge $N$, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states, the SSP is answered negatively with probability one for almost all $N$. Using a witness to the failure of symmetric separability, namely the number entanglement (NE) introduced in arXiv:2110.09388, we show that most symmetric and separable states are actually far from being symmetrically separable, with the NE featuring Gaussian concentration around a strictly positive mean value. We discuss some consequences of our results for quantum tasks in the presence of a superselection rule or in the absence of a common reference frame. Progress is made on the question of the size of the separable space constrained by $N$. We also touch upon the question of the complexity of SSP, and multiparty entanglement.
Source: arXiv (Cornell University)
Authors: Boudreault, Christian, Levasseur, Nicolas
Institutions: Royal Military College Saint-Jean, Université de Montréal
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Canadian Defence Academy
OpenAlex ID: W7140170530