Such stuff as magic is made on: compact operator algebra, stabilizer polytope and the structure of reduced density matrices in a Kitaev spin liquid

• URL: http://arxiv.org/abs/2609.03485v1
• Date: Thu, 03 Sep 2026 07:44:08 GMT
• Title: Such stuff as magic is made on: compact operator algebra, stabilizer polytope and the structure of reduced density matrices in a Kitaev spin liquid
• Abstract summary: We investigate the onset of magic within subsystems of a larger many-body quantum system.<n>We show that intricate structures emerge which shed important light on the underlying many-body physics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum many-body systems exhibit rich and complex behaviour. Magic has recently emerged as a powerful new diagnostic for probing such systems, complementing other key features such as many-body entanglement. Here, starting from an investigation of the onset of magic within subsystems of a larger many-body quantum system, we show that intricate structures emerge which shed important light on the underlying many-body physics. Focusing on the Kitaev honeycomb model, we first identify the temperature below which local subsystems acquire magic. Remarkably, we find that the optimal magic witnesses active at the onset of magic reveal compact operator spaces that continue to capture the local thermal states throughout their subsequent evolution. For the six-site hexagonal marginal, this connection can be made stronger: the same operator space emerges independently from the symmetries of the local marginal and forms the symmetry-resolved plaquette algebra. When these symmetries are realized exactly, the local state lies entirely within this algebra and the reduced robustness of magic is equal to the full robustness of magic. The same reduced description can also be applied to other local quantum resources, which we illustrate using genuine multipartite entanglement. Furthermore, the operator spaces possess a rich algebraic structure in the form of finite-dimensional Euclidean Jordan algebras, with a natural interpretation in terms of bond and bond-cycle operators. Our general methodology therefore show how the onset of local magic can reveal a compact, physically meaningful operator structure underlying the finite-temperature Kitaev spin liquid, and opens up a new avenue towards reduced descriptions of quantum resources in many-body systems.

Related papers

• Quantum resource redistribution drives spectral splits in dense neutrino gases [0.0]
  We characterize the quantum resource landscape of collective neutrino oscillations using entanglement entropy, non-local magic, and matrix product state bond dimension.<n>Using tensor network simulations of neutrinos in the two-flavor sector, we demonstrate that spectral splits--sharp energy-dependent flavor swaps--emerge precisely where entanglement entropy is maximized and non-local magic is minimized locally.
  arXiv  Detail & Related papers  (2026-05-22T12:54:10Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Multipartite Non-local Magic and SYK Model [0.0]
  We investigate the structure of quantum magic in interacting disordered fermionic systems.<n>We introduce a multipartite non-local magic functional, constructed from an inclusion-exclusion combination of subsystem contributions.<n>We show that while fortuitous BPS states exhibit intermediate stabilizer complexity, the multipartite measure unveils a rich, sector-dependent pattern of global correlations.
  arXiv  Detail & Related papers  (2026-01-06T15:04:10Z)
• Magic spreading under unitary Clifford dynamics [0.0]
  We study the dynamics of locally injected magic in unitary Clifford circuits.<n>We show that the spatial distribution of magic can be inferred from a canonical representation of low-magic states.<n>We numerically establish that, at early times, both length scales grow ballistically at distinct velocities set by the entanglement velocity.
  arXiv  Detail & Related papers  (2025-11-26T15:20:15Z)
• Mpemba Effects in Quantum Complexity [39.146761527401424]
  We study the dynamics of coherence, imaginarity, non-Gaussianity, and magic state resources in random circuit models.<n>Our results reveal that coherence and imaginarity display a quantum Mpemba effect when the system is in resourceful product states.<n>All four resources exhibit the so-called Pontus-Mpemba effect: an initial "preheating" stage accelerates relaxation compared to direct "cooling" dynamics.
  arXiv  Detail & Related papers  (2025-09-26T10:35:05Z)
• The Large-Scale Structure of Entanglement in Quantum Many-body Systems [44.99833362998488]
  We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems.<n>In particular, we show that every gapped phase of matter, even the trivial one, in $Dgeq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement.
  arXiv  Detail & Related papers  (2025-03-05T19:01:05Z)
• Harnessing Chiral Spin States in Molecular Nanomagnets for Quantum Technologies [44.1973928137492]
  We show that chiral qubits naturally suppress always-on interactions that can not be switched off in weakly coupled qubits.<n>Our findings establish spin chirality engineering as a promising strategy for mitigating always-on interaction in entangling two chiral qubits in molecular quantum technologies.
  arXiv  Detail & Related papers  (2025-01-21T08:23:12Z)
• Magic spreading in random quantum circuits [0.0]
  We show how rapidly do generic many-body dynamics generate magic resources under the constraints of locality and unitarity.<n>We demonstrate that magic resources equilibrate on timescales logarithmic in the system size, akin to anti-concentration and Hilbert space delocalization phenomena.<n>As random circuits are minimal models for chaotic dynamics, we conjecture that our findings describe the phenomenology of magic resources growth in a broad class of chaotic many-body systems.
  arXiv  Detail & Related papers  (2024-07-04T13:43:46Z)
• Exploring Hilbert-Space Fragmentation on a Superconducting Processor [23.39066473461786]
  Isolated interacting quantum systems generally thermalize, yet there are several counterexamples for the breakdown of ergodicity. Recently, ergodicity breaking has been observed in systems subjected to linear potentials, termed Stark many-body localization. Here, we experimentally explore initial-state dependent dynamics using a ladder-type superconducting processor with up to 24 qubits.
  arXiv  Detail & Related papers  (2024-03-14T04:39:14Z)
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension [44.41126861546141]
  We provide a classification of Lie algebras generated by translation-invariant 2-local spin chain Hamiltonians. We consider chains with open and periodic boundary conditions and find 17 unique dynamical Lie algebras. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches.
  arXiv  Detail & Related papers  (2023-09-11T17:59:41Z)
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories [0.0]
  We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains. We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from. We provide conclusive evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes.
  arXiv  Detail & Related papers  (2023-05-29T18:14:47Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)

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.