Pure-state entanglement rests on a single algebraic backbone: majorization of the Schmidt spectrum governs state conversion under local operations and classical communication, and constrains entanglement monotones. Here we establish a corresponding majorization law for fermionic non-Gaussianity, the resource that elevates free fermions to universal quantum computation. Under any fermionic Gaussian protocol with pure state outcomes, the Williamson spectrum of a pure state's Majorana covariance matrix is weakly majorized by its ensemble average. This spectral law mirrors that of entanglement theory. It turns computable non-Gaussianity quantifiers such as fermionic antiflatness and occupation entropies into strong monotones for fermionic non-Gaussianity, and delivers necessary conditions and converse bounds on state conversion under Gaussian protocols. When fermion parity is conserved, no catalyst can remove a majorization obstruction---unless it carries parity coherence---and asymptotic interconversion is irreversible already for pure states. All relevant quantities are accessible from two-point Majorana correlators, turning the theory developed here into experimentally observable properties of quantum matter, testable on present-day quantum devices.
Fermionic Gaussian states form a central class of classically tractable quantum states, while fermionic non-Gaussianity provides the resource required to go beyond free-fermion dynamics. A key challenge is to quantify this resource through monotones that are both mathematically rigorous and experimentally accessible. H...
Nonlocal nonstabilizerness quantifies the irreducible magic resource encoded in bipartite entanglement, but its evaluation is generally hindered by a highly nonconvex optimization over local unitary transformations. Here we propose a Schmidt-reference-state framework that replaces this optimization by a direct construc...
Absolutely maximally entangled states represent a highly constrained form of multipartite entanglement and play an important role in quantum information theory. We investigate a weaker form of uniformity of entanglement for four-party systems of local dimension $d>2$ that requires the three balanced bipartitions to hav...
We introduce a mapping between the ground state of interacting fermionic Hamiltonians and the non-equilibrium steady state of a purely dissipative open quantum system. Within the framework of third quantization, we map the Fermi-Hubbard Hamiltonian onto Lindblad jump operators acting on Majorana fermions. Remarkably, b...
How a quantum state responds to small parameter changes underlies state distinguishability, many-body response, and metrological sensitivity. The Pauli probability spectrum provides a natural description of many-body quantum states, but it is not evident how much of this response survives in the corresponding classical...
The manipulation of quantum entanglement is fundamentally irreversible: some mixed entangled states require pure entanglement for their preparation, although no pure entanglement can be recovered from them by local operations and classical communication. This irreversibility is known to persist even under the maximal c...
Tulja Varun Kondra, Raphael Brinster, H. Kampermann et al.· 0 citations
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