The topological spectrum of high dimensional quantum states

• URL: http://arxiv.org/abs/2503.12540v1
• Date: Sun, 16 Mar 2025 15:13:24 GMT
• Title: The topological spectrum of high dimensional quantum states
• Authors: Robert de Mello Koch, Pedro Ornelas, Neelan Gounden, Bo-Qiang Lu, Isaac Nape, Andrew Forbes,
• Abstract summary: Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves.<n>Here, we harness the synthetic dimensions of orbital angular momentum to discover a rich tapestry of topological maps in high dimensional spaces.<n>We show that the topological spectrum allows the simultaneous ability to be robust to and probe for perturbation, the latter made possible by observing emergent signatures in the non-topological (trivial) spaces of the spectrum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can be characterised by a single topological number, e.g., a Chern number in matter or a Skyrme number in waves. Here, using photonic quantum states as an example, we harness the synthetic dimensions of orbital angular momentum (OAM) to discover a rich tapestry of topological maps in high dimensional spaces. Moving beyond spin textured fields, we demonstrate topologies using only one degree of freedom, the OAM of light. By interpreting the density matrix as a non-Abelian Higgs potential, we are able to predict topologies that exist as high dimensional manifolds which remarkably can be deconstructed into a multitude of simpler maps from disks to disks and spheres to spheres, giving rise to the notion of a topological spectrum rather than a topological number. We confirm this experimentally using quantum wave functions with an underlying topology of 48 dimensions and a topological spectrum spanning over 17000 maps, an encoding alphabet with enormous potential. We show that the topological spectrum allows the simultaneous ability to be robust to and probe for perturbation, the latter made possible by observing emergent signatures in the non-topological (trivial) spaces of the spectrum. Our experimental approach benefits from easy implementation, while our theoretical framework is cast in a manner that can be extrapolated to any particle type, dimension and degree of freedom. Our work opens exciting future possibilities for quantum sensing and communication with topology.

Related papers

• Topological QBits in Flux-Quantized Super-Gravity [0.0]
  We give a brief exposition of our recent realization of anyonic quantum states on single M5-brane probes in 11D super-gravity backgrounds. We end with some more meta-physical remarks on (cohesive) homotopy (type) theory in view of emergent fundamental physics and, possibly, M-theory.
  arXiv  Detail & Related papers  (2024-11-01T14:37:12Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function [4.097395387450313]
  topological entanglement entropy can be used to detect nontrivial topological order from a ground state wave function. We propose a simple entanglement-based protocol for extracting the quantum dimensions of all anyons from a single ground state wave function in two dimensions. This protocol is validated in the continuum and verified on lattices, and we anticipate it to be realizable in various quantum simulation platforms.
  arXiv  Detail & Related papers  (2023-04-26T01:54:21Z)
• Overlapping qubits from non-isometric maps and de Sitter tensor networks [41.94295877935867]
  We show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom. We highlight how approximate overlapping qubits are conceptually connected to Hilbert space dimension verification, degree-of-freedom counting in black holes and holography.
  arXiv  Detail & Related papers  (2023-04-05T18:08:30Z)
• Topological Quantum Programming in TED-K [0.0]
  We describe a fundamental and natural scheme that we are developing, for typed functional (hence verifiable) topological quantum programming. It reflects the universal fine technical detail of topological q-bits, namely of symmetry-protected (or enhanced) topologically ordered Laughlin-type anyon ground states. The language system is under development at the "Center for Quantum and Topological Systems" at the Research Institute of NYU, Abu Dhabi.
  arXiv  Detail & Related papers  (2022-09-17T14:00:37Z)
• Topological multi-mode waveguide QED [49.1574468325115]
  We show how to take advantage of topologically protected propagating modes by interfacing them with quantum emitters. Such capabilities pave the way for generating quantum gates among topologically protected photons as well as generating more complex entangled states of light in topological channels.
  arXiv  Detail & Related papers  (2022-07-05T14:48:50Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Quantum Hall phase emerging in an array of atoms interacting with photons [101.18253437732933]
  Topological quantum phases underpin many concepts of modern physics. Here, we reveal that the quantum Hall phase with topological edge states, spectral Landau levels and Hofstadter butterfly can emerge in a simple quantum system. Such systems, arrays of two-level atoms (qubits) coupled to light being described by the classical Dicke model, have recently been realized in experiments with cold atoms and superconducting qubits.
  arXiv  Detail & Related papers  (2020-03-18T14:56:39Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.