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The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970's, and only proved very recently, that there is a multitude of further constraints on these…
Postulated by Pauli to explain the electronic structure of atoms and molecules, the exclusion principle establishes an upper bound of 1 for the fermionic natural occupation numbers $\{n_i\}$. A recent analysis of the pure…
Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are even stronger restricted by so-called generalized Pauli constraints. Whenever given natural occupation numbers lie on the boundary of the allowed…
Fermionic natural occupation numbers do not only obey Pauli's exclusion principle, but are even further restricted by so-called generalized Pauli constraints. Such restrictions are particularly relevant whenever they are saturated by given…
Analytical evidence for the physical relevance of generalized Pauli constraints (GPCs) has recently been provided in [PRL 110, 040404]: Natural occupation numbers $\vec{\lambda}\equiv (\lambda_i)$ of the ground state of a model system in…
The Pauli exclusion principle as constraint on fermionic occupation numbers is a consequence of the much deeper fermionic exchange statistics. Just recently, it was shown by Klyachko that this antisymmetry of fermionic wave functions leads…
The question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of…
The role of the generalized Pauli constraints (GPCs) in higher spatial dimensions and by incorporating spin degrees of freedom is systematically explored for a system of interacting fermions confined by a harmonic trap. Physical relevance…
All matter is made up of fermions -- one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state. Antisymmetry of the…
We have explained and comprehensively illustrated in Part I that the generalized Pauli constraints suggest a natural extension of the concept of active spaces. In the present Part II, we provide rigorous derivations of the theorems involved…
Recently it was suggested that the neutrino may violate the Pauli exclusion Principle (PEP). This renews interest in the systematic search for bilinear commutation relations that could describe deviations from PEP. In the context of this…
The concept of active spaces simplifies the description of interacting quantum many-body systems by restricting to a neighbourhood of active orbitals around the Fermi level. The respective wavefunction ansatzes which involve all possible…
This paper is a revision of the combinatorics of fractional exclusion statistics (FES). More specifically, the following exact statement of the generalized Pauli principle is derived: for an $N$-particles system exhibiting FES of extended…
The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or…
A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to…
The dependence of the (quasi-)saturation of the generalized Pauli constraints on the pair potential is studied for ground states of few-fermion systems. For this, we consider spinless fermions in one dimension which are harmonically…
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be…
We establish a toolbox for studying and applying spin-adapted generalized Pauli constraints (GPCs) in few-electron quantum systems. By exploiting the spin symmetry of realistic $N$-electron wave functions, the underlying one-body pure…
Pauli's exclusion principle has a strong impact on the properties of most fermionic quantum systems. Remarkably, the fermionic exchange symmetry implies further constraints on the one-particle picture. By exploiting those generalized Pauli…
The natural occupation numbers of fermionic systems are subject to non-trivial constraints, which include and extend the original Pauli principle. A recent mathematical breakthrough has clarified their mathematical structure and has opened…