Bounding the entanglement of a state from its spectrum

• URL: http://arxiv.org/abs/2604.02420v1
• Date: Thu, 02 Apr 2026 18:00:04 GMT
• Title: Bounding the entanglement of a state from its spectrum
• Abstract summary: We characterize the set of states whose entanglement content cannot be increased under any unitary.<n>Our approach yields analytical and practical criteria for quantifying the entanglement content of full-rank states in arbitrary dimensions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any unitary. By employing linear maps (and their inverses), we derive constraints on the achievable degree of entanglement from the spectrum of the density matrix. In particular, we focus on the negativity and the Schmidt number. Our approach yields analytical and practical criteria for quantifying the entanglement content of full-rank states in arbitrary dimensions using only a subset of their eigenvalues. Moreover, some of the derived conditions can be used to bound the spectra of Schmidt number witnesses.

Related papers

• Boltzmann counting in Hilbert space [39.146761527401424]
  We introduce a geometric entropy for quantum preparations, defined as the logarithm of the Hilbert-space volume of pure states compatible with a given set of constraints.<n>We analyze three classes of constraints: restriction to a subspace, fixed expectation values, and coarse-grained subsystem descriptions.<n>The resulting framework provides a geometric measure of quantum ignorance at the level of the preparation.
  arXiv  Detail & Related papers  (2026-08-20T15:01:51Z)
• Gaussian fermionic embezzlement of entanglement [41.321581612257056]
  We show that the embezzling property is in fact a generic property of fermionic Gaussian states.<n>We bridge finite-size systems to abstract characterizations based on the classification of von Neumann algebras.
  arXiv  Detail & Related papers  (2025-09-19T08:26:03Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses [0.0]
  Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set.<n>We employ linear maps and their inverses to derive new sufficient analytical conditions for absolute separability in arbitrary dimensions.<n>We refine the characterization of the set when multiple non-comparable criteria for absolute separability are available.
  arXiv  Detail & Related papers  (2024-10-29T18:00:04Z)
• Absolute dimensionality of quantum ensembles [41.94295877935867]
  The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis.<n>We propose an absolute, i.e.basis-independent, notion of dimensionality for ensembles of quantum states.
  arXiv  Detail & Related papers  (2024-09-03T09:54:15Z)
• Distribution of the entanglement entropy of a non-ergodic quantum state [0.0]
  We theoretically derive the probability densities of the entanglement measures of a pure non-ergodic many-body state.<n>Our results indicate significant fluctuations of the measures around their average behavior.<n>The information is relevant not only for hierarchical arrangement of entangled states but also for phase transition studies of many body systems.
  arXiv  Detail & Related papers  (2024-02-02T02:38:01Z)
• Unfolding a composed ensemble of energy spectra using singular value decomposition [0.0]
  We show that singular value decomposition can be used even for the challenging situations where the ensemble is composed out of realizations originating from a different range of parameters resulting in a non-monotonous local density of states.
  arXiv  Detail & Related papers  (2023-03-08T17:40:50Z)
• Entanglement phase diagrams from partial transpose moments [0.0]
  We analyze the entanglement properties of bipartite reduced states of a tripartite pure state. We show that this ratio takes well-defined values in the thermodynamic limit for various families of entangled states. Our results can be used to experimentally test necessary conditions for different types of mixed-state randomness.
  arXiv  Detail & Related papers  (2022-12-20T11:39:02Z)
• Emergence of Fermi's Golden Rule [55.73970798291771]
  Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a continuum of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing.
  arXiv  Detail & Related papers  (2022-06-01T18:35:21Z)
• Quantifying entanglement of parametric down-converted states in all degrees of freedom [0.0]
  We quantify the amount of entanglement by the Schmidt number of the state, represented as a pure bipartite state. A quantitative example with reasonably achievable experimental conditions is considered to demonstrate that extremely large Schmidt numbers are achievable.
  arXiv  Detail & Related papers  (2020-04-14T10:51:28Z)
• Partial Traces and the Geometry of Entanglement; Sufficient Conditions for the Separability of Gaussian States [0.0]
  We put an emphasis on the geometrical properties of the covariance ellipsoids of the reduced states. We give new and easily numerically implementable sufficient conditions for the separability of all Gaussian states.
  arXiv  Detail & Related papers  (2020-03-30T02:22:08Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.