Non-Local Magic from the Entanglement Spectrum

• URL: http://arxiv.org/abs/2607.07808v1
• Date: Wed, 08 Jul 2026 18:00:16 GMT
• Title: Non-Local Magic from the Entanglement Spectrum
• Abstract summary: We show that non-local magic can be upper-bounded by an entanglement entropy.<n>Our results identify the spectral organization of the entanglement spectrum as the key ingredient governing non-local magic.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-local magic has recently emerged as a fundamental resource for characterizing genuinely non-local non-stabilizer correlations. However, its direct calculation is an intractable numerical problem, except for small systems, and its understanding remains limited. We derive a representation of non-local magic in terms of the Walsh--Hadamard autocorrelations of the entanglement spectrum. Our representation makes the underlying harmonic structure explicit and enables a systematic analysis of its behaviors for various scenarios. We prove that non-local magic can be upper-bounded by an entanglement entropy and we derive exact analytical results for broad classes of quantum states, characterizing the scaling of non-local magic for volume-law states, as well as ground states of one-dimensional gapped and critical systems. Our results identify the spectral organization of the entanglement spectrum as the key ingredient governing non-local magic and provide a framework for further systematic analytical investigation.

Related papers

• Non-local Magic: closed-form solution and equivalence with magic of purification [0.9481925300137773]
  Non-local magic quantifies the non-stabilizerness of a bipartite quantum state that cannot be removed by local unitary transformations.<n>We introduce the magic of purification, defined as the minimum pure-state magic over all purifications of a mixed state.<n>We prove that non-local magic coincides with the minimum magic of purification along the unitary orbit of the reduced density operator.
  arXiv  Detail & Related papers  (2026-09-03T17:21:11Z)
• Exact quantification of nonlocal magic [0.0]
  We show how the entanglement spectrum spreads its weight across factor-of-two windows of rank.<n>Nonlocal magic becomes an operationally meaningful property of quantum correlations.
  arXiv  Detail & Related papers  (2026-08-28T17:40:56Z)
• Schmidt-Gauge Non-Local Magic: Representation, Optimality, and Mathematical Properties [0.0]
  We develop the mathematical theory associated with the Schmidt-gauge formulation of non-local magic.<n>We derive general analytical properties of Schmidt-gauge non-local magic, including entanglement bounds, selection rules, and exact relations with the moments of the normalized Walsh spectrum.<n>This representation also provides an interpretation of Schmidt-gauge non-local magic as a logarithmic inverse participation ratio normalized by a universal harmonic baseline.
  arXiv  Detail & Related papers  (2026-08-03T18:00:12Z)
• Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory [37.724232080494424]
  Entanglement and non-stabilizerness (magic) quantify two distinct departures of quantum systems from classical description.<n>We calculate entanglement entropy and stabilizer Rényi entropy of the ground state of the (1+1)-dimensional SU(2) lattice gauge theory.<n>We find a crossover denoted by $g_star$ where the ground state passes from a more magic-rich regime into a regime with less magic.
  arXiv  Detail & Related papers  (2026-06-08T18:00:00Z)
• Observation of Universal Spectral Moments and the Dynamic Dispersive-to-Proliferative Transition [22.500854615463314]
  spectral moments provide boundary-robust bulk observables in finite non-Hermitian lattices.<n>We show that local bulk dynamics can remain stable (dispersive) even in a $mathcalPT$-broken spectral regime.<n>These results establish spectral moments as practical bulk descriptors for finite non-Hermitian matter.
  arXiv  Detail & Related papers  (2026-04-30T08:38:46Z)
• Non-Local Magic Resources for Fermionic Gaussian States [0.0]
  Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems.<n>We propose a closed-form expression for the non-local stabilizer entropies of fermionic Gaussian states over local Gaussian unitaries.<n>We apply this framework to characterize fermionic non-local magic across diverse physical regimes.
  arXiv  Detail & Related papers  (2026-04-29T18:00:00Z)
• Analytic formulae for non-local magic in bipartite systems of qutrits and ququints [0.0]
  We conjecture analytic expressions for the non-local magic of bipartite pure qudit states of prime local dimension.<n>For composite local dimensions, we find that the analogous expressions do not in general reproduce the global minimum.
  arXiv  Detail & Related papers  (2026-03-10T03:46:02Z)
• On the Spectral Flattening of Quantized Embeddings [25.64641307046705]
  Training Large Language Models at ultra-low precision is critically impeded by instability rooted in the conflict between discrete quantization constraints and the intrinsic heavy-tailed spectral nature of linguistic data.<n>This work not only quantifies the spectral sensitivity of LLMs but also establishes spectral fidelity as a necessary condition for stable low-bit optimization.
  arXiv  Detail & Related papers  (2026-02-01T02:21:53Z)
• Advantage of utilizing nonlocal magic resource in Haar-random circuits [13.89684973179205]
  In design and simulation of quantum circuits with multiple units, the computational ability is greatly limited by quickly increasing entanglement.<n>We uncover an intrinsic scaling law of the nonlocal magic resource and the bond dimension of matrix product states in Haar-random quantum circuits.
  arXiv  Detail & Related papers  (2025-09-30T14:48:55Z)
• Grounding the Ungrounded: A Spectral-Graph Framework for Quantifying Hallucinations in Multimodal LLMs [19.099044165107696]
  We present a rigorous, information-geometric framework in diffusion dynamics that quantifies hallucination in MLLMs.<n>We derive Courant--Fischer bounds on a temperature-dependent hallucination energy and use RKHS eigenmodes to obtain modality-aware, interpretable measures.
  arXiv  Detail & Related papers  (2025-08-26T18:54:52Z)
• Magic phase transitions in monitored gaussian fermions [37.742691394718086]
  We show how monitoring affects magic state resources, the nonstabilizerness, of Gaussian fermionic systems.<n>This measurement-induced complexity transition highlights the power of magic-based diagnostics in revealing hidden features of monitored many-body dynamics.
  arXiv  Detail & Related papers  (2025-07-09T18:00:02Z)
• Gravitational back-reaction is magical [5.61965899768974]
  We show that non-local magic is lower bounded by the non-flatness of entanglement spectrum and upper bounded by the amount of entanglement in the system.<n>In conformal field theories, we conjecture that the non-local magic should scale linearly with entanglement entropy but sublinearly when an approximation of the state is allowed.
  arXiv  Detail & Related papers  (2024-03-11T18:00:03Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)

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.