Non-isometry, State-Dependence and Holography

• URL: http://arxiv.org/abs/2411.07296v1
• Date: Mon, 11 Nov 2024 19:00:05 GMT
• Title: Non-isometry, State-Dependence and Holography
• Authors: Stefano Antonini, Vijay Balasubramanian, Ning Bao, ChunJun Cao, Wissam Chemissany,
• Abstract summary: We establish an equivalence between non-isometry of quantum codes and state-dependence of operator reconstruction. We show that, assuming known gravitational path integral results for overlaps between semiclassical states, non-isometric bulk-to-boundary maps with a trivial kernel are approximately isometric. We conjecture that, under certain physical assumptions for the definition of the Hilbert space of effective field theory in AdS space, the presence of a global horizon implies a non-isometric global bulk-to-boundary map.
• Score: 0.09320657506524146
• License:
• Abstract: We establish an equivalence between non-isometry of quantum codes and state-dependence of operator reconstruction, and discuss implications of this equivalence for holographic duality. Specifically, we define quantitative measures of non-isometry and state-dependence and describe bounds relating these quantities. In the context of holography we show that, assuming known gravitational path integral results for overlaps between semiclassical states, non-isometric bulk-to-boundary maps with a trivial kernel are approximately isometric and bulk reconstruction approximately state-independent. In contrast, non-isometric maps with a non-empty kernel always lead to state-dependent reconstruction. We also show that if a global bulk-to-boundary map is non-isometric, then there exists a region in the bulk which is causally disconnected from the boundary. Finally, we conjecture that, under certain physical assumptions for the definition of the Hilbert space of effective field theory in AdS space, the presence of a global horizon implies a non-isometric global bulk-to-boundary map.

Related papers

• 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)
• A holographic view of topological stabilizer codes [0.6290982779160698]
  We provide an explicit and general framework for understanding the bulk-boundary correspondence in Pauli topological stabilizer codes. We show that the boundary Hilbert space cannot be realized via local degrees of freedom. We show how linear and fractal subsystem symmetries naturally arise at the boundaries of fracton phases.
  arXiv  Detail & Related papers  (2023-12-07T19:00:00Z)
• Non-Hermitian extended midgap states and bound states in the continuum [0.0]
  We find two flavours of bound states in the continuum, both stable even in the absence of chiral symmetry. Results clarify fundamental aspects of topology, and symmetry in the light of different approaches to the anomalous non-Hermitan bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2023-10-27T16:58:04Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Holographic properties of superposed quantum geometries [0.0]
  We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data. This class includes spin networks, the kinematic states of lattice gauge theory and discrete quantum gravity.
  arXiv  Detail & Related papers  (2022-07-15T17:37:47Z)
• Modest holography and bulk reconstruction in asymptotically flat spacetimes [0.0]
  We present a "modest" holographic reconstruction of the bulk geometry in unrelatedally flat spacetime using the two-point correlators of quantum field theory (QFT) The bulk reconstruction relies on two results: (i) there is a bulk-to-boundary type correspondence between free quantum fields living in the bulk manifold and free quantum fields living on its null boundary, and (ii) one can construct the metric by making use of the Hadamard expansion of the field living in the bulk.
  arXiv  Detail & Related papers  (2022-04-27T18:00:56Z)
• Holographic maps from quantum gravity states as tensor networks [0.0]
  We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism. The maps are defined in terms of a partition of the quantum geometric data associated to an open graph into bulk and boundary ones.
  arXiv  Detail & Related papers  (2021-05-13T17:53:00Z)
• Long-distance entanglement of purification and reflected entropy in conformal field theory [58.84597116744021]
  We study entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy. We find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour.
  arXiv  Detail & Related papers  (2021-01-29T19:00:03Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• Geometry of Similarity Comparisons [51.552779977889045]
  We show that the ordinal capacity of a space form is related to its dimension and the sign of its curvature. More importantly, we show that the statistical behavior of the ordinal spread random variables defined on a similarity graph can be used to identify its underlying space form.
  arXiv  Detail & Related papers  (2020-06-17T13:37:42Z)

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.