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 fermionic wave function, however, implies additional constraints on the natural occupation numbers. These constraints depend on the dimensionality and purity of the system and have so far not been explored experimentally in a fermionic system to our best knowledge. Here we propose an experiment in a multi-quantum-dot system capable of producing the highly entangled fermionic states necessary to reach the regime, where these additional constraints become dominant and can be probed. The type and strength of the required multifermion entanglement provides barriers to reaching deep into this regime. Transcending these barriers thus serves as a testing ground for the capabilities of future fermionic quantum information processing as well as quantum computer architectures based on fermionic states. All operations in our proposal are based on all-optical gates presented in Li and Akopian [arXiv:2107.05960 (2021)]. We simulate our state preparation procedures in realistic structures, including all main decoherence sources, and find fidelities above 0.97.
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 fermionic wave function, however, implies additional constraints on the natural occupation numbers. These constraints depend on the dimensionality and purity of the system and have so far not been explored experimentally in a fermionic system to our best knowledge. Here we propose an experiment in a multi-quantum-dot system capable of producing the highly entangled fermionic states necessary to reach the regime, where these additional constraints become dominant and can be probed. The type and strength of the required multifermion entanglement provides barriers to reaching deep into this regime. Transcending these barriers thus serves as a testing ground for the capabilities of future fermionic quantum information processing as well as quantum computer architectures based on fermionic states. All operations in our proposal are based on all-optical gates presented in Li and Akopian [arXiv:2107.05960 (2021)]. We simulate our state preparation procedures in realistic structures, including all main decoherence sources, and find fidelities above 0.97.
Abstract “What are the consequences… that Fermi particles cannot get into the same state…” R. P. Feynman wrote of the Pauli exclusion principle, “In fact, almost all the peculiarities of the material world hinge on this wonderful fact.” In 1972 Borland and Dennis showed that there exist powerful constraints beyond the Pauli exclusion principle on the orbital occupations of Fermi particles, providing important restrictions on quantum correlation and entanglement. Here we use computations on quantum computers to experimentally verify the existence of these additional constraints. Quantum many-fermion states are randomly prepared on the quantum computer and tested for constraint violations. Measurements show no violation and confirm the generalized Pauli exclusion principle with an error of one part in one quintillion.
The Pauli exclusion principle is a fundamental law underpinning the structure of matter. Because of their antisymmetric wave function, no two fermions can occupy the same quantum state. Here, we report on the direct observation of the Pauli principle in a continuous system of up to six particles in the ground state of a two-dimensional harmonic oscillator. To this end, we sample the full many-body wave function by applying a single atom resolved imaging scheme in momentum space. We find so-called Pauli crystals as a manifestation of higher order correlations. In contrast to true crystalline phases, these unique high-order density correlations emerge even without any interactions present. Our work lays the foundation for future studies of correlations in strongly interacting systems of many fermions.
The concept of entanglement in many‑body physics has traditionally focused on spin or particle‑number degrees of freedom. Here we introduce a novel class of fermionic quantum phases in which orbital degrees of freedom of identical particles become entangled across spatially distinct sites. We construct the general form of the many‑body wavefunction for a system of N fermions occupying L orbitals per site, and show that the ground state of certain interacting Hamiltonians can be written as |\Psi> = \sum_{i,j} c_{ij} | \phi_i \phi_j >, where | \phi_i > and | \phi_j > denote single‑particle orbital states localized at different lattice sites. This entangled orbital structure leads to emergent properties distinct from conventional band insulators, Mott insulators, or spin liquids. We discuss the symmetry constraints, the role of fermionic statistics, and the topological aspects that arise when the orbital entanglement is global. Theoretical analysis predicts that FOEPs can host protected edge modes, exotic quasiparticles, and non‑Abelian statistics in two‑dimensional lattices. We also outline experimental signatures that could be observed in engineered cold‑atom systems, photonic lattices, or layered transition‑metal dichalcogenides, and argue that the discovery of FOEPs would open a new frontier in the search for quantum materials with high‑temperature superconductivity or quantum information processing capabilities.
Since typically the physics of many body quantum systems is solely described and determined by pairwise interactions, the concept of reduced particle information is fundamentally relevant, particularly for indistinguishable particles. Determining the compatibility of r-particle reduced density operators (r-RDOs) with some N-particle state is known as the N-representability problem. The Pauli exclusion principle provides a set of necessary and sufficient conditions for the N-representability of fermionic 1-RDOs. However, pure N-representability requires a set of stricter conditions which are known as Generalised Pauli constraints (GPCs). In this thesis we investigate the influence and significance of the GPCs beyond the well-explored and established relevance of the Pauli exclusion principle. In particular, we analytically study the (quasi-)pinning effect which corresponds to a saturation of the GPCs and imposes structural simplifications on the N-fermion state. So far, nothing is known about its origin and mechanisms. We will close this gap by analytically examining the dependence of quasipinning on the particle number, the dimensionality and the spin polarisation in a representative physical model system. Our results suggest the notion of a microscopic Pauli pressure which is a consequence of the competition between energy minimisation and antisymmetry, and drives the system towards the boundary of the allowed region. Furthermore, the relevance of quasipinning beyond the wellknown Pauli exclusion principle is evaluted by the Q-measure. The outcomes provide first direct evidence for the need to incorporate GPCs into the physical description. To explore the role of the fermionic exchange symmetry beyond the Pauli exclusion principle from a more general perspective, we consider systems of hardcore bosons. Indeed, they exhibit a (lattice-based) exclusion principle, although their exchange symmetry is bosonic. Occupation numbers on oneparticle states other than the lattice basis can exceed one. We prove that the maximal occupation number is given by λmax = N/d(d - N + 1) where N, d are the numbers of particles and lattice sites. In addition, we derive necessary conditions for the N-representability of hardcore boson 1-RDOs and investigate the one-particle entropy boundaries. Finally, we present one-dimensional physical systems which macroscopically saturate λmax and exhibit (fractional) Bose-Einstein condensation.
The Pauli exclusion principle is one of the fundamental laws of modern physics. It determines the structure of atoms, the stability of matter, the properties of fermionic systems, and macroscopic phenomena ranging from chemistry to astrophysics. In standard quantum mechanics (QM), this principle is formulated as an axiom of antisymmetry: the wave function of two fermions must change sign under the exchange of coordinates. However, the origin of this antisymmetry remains unexplained within QM itself. Within ZEBTS — the Law of Unity of Being of the Triune Substance — the Pauli principle acquires a geometric and topological foundation. In this ontology, fermions are not treated as elementary particles but as topological modes of the operator metric, arising from the spectral structure of quantum geometry. Antisymmetry and the prohibition of identical states emerge as consequences of: the non‑commutativity of the operator metric, the topological charge λ, the spectral non‑intersection of eigenvalues, holographic constraints on information density. Thus, ZEBTS derives the Pauli principle as a topological law of quantum geometry, rather than a postulate.
Quantum computers are expected to become a powerful tool for studying physical quantum systems. Consequently, a number of quantum algorithms for studying the physical properties of such systems have been developed. While qubit-based quantum computers are naturally suited to the study of spin-1/2 systems, systems containing other degrees of freedom must first be encoded into qubits. Transformations to and from fermionic degrees of freedom have long been an important tool in physics and, now the simulation of fermionic systems on quantum computers based on qubits provides yet another application. In this perspective, we review methods for encoding fermionic degrees of freedom into qubits and attempt to dispel the persistent notion that fermionic systems beyond one dimension are fundamentally more difficult to deal with.