Euclidean and complex geometries from real-time computations of gravitational Rényi entropies

• URL: http://arxiv.org/abs/2409.17428v1
• Date: Wed, 25 Sep 2024 23:32:49 GMT
• Title: Euclidean and complex geometries from real-time computations of gravitational Rényi entropies
• Authors: Jesse Held, Xiaoyi Liu, Donald Marolf, Zhencheng Wang,
• Abstract summary: We show that the appropriate real-time path integral yields both R'enyi entropies and associated complex saddle-point geometries that agree with Euclidean methods. After brief explanations of these general points, we use JT gravity to illustrate the associated real-time computations in detail.
• Score: 1.3392361199400264
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gravitational R\'enyi computations have traditionally been described in the language of Euclidean path integrals. In the semiclassical limit, such calculations are governed by Euclidean (or, more generally, complex) saddle-point geometries. We emphasize here that, at least in simple contexts, the Euclidean approach suggests an alternative formulation in terms of the bulk quantum wavefunction. Since this alternate formulation can be directly applied to the real-time quantum theory, it is insensitive to subtleties involved in defining the Euclidean path integral. In particular, it can be consistent with many different choices of integration contour. Despite the fact that self-adjoint operators in the associated real-time quantum theory have real eigenvalues, we note that the bulk wavefunction encodes the Euclidean (or complex) R\'enyi geometries that would arise in any Euclidean path integral. As a result, for any given quantum state, the appropriate real-time path integral yields both R\'enyi entropies and associated complex saddle-point geometries that agree with Euclidean methods. After brief explanations of these general points, we use JT gravity to illustrate the associated real-time computations in detail.

Related papers

• A unified approach to quantum de Finetti theorems and SoS rounding via geometric quantization [0.0]
  We study a connection between a Hermitian version of the SoS hierarchy, related to the quantum de Finetti theorem. We show that previously known HSoS rounding algorithms can be recast as quantizing an objective function.
  arXiv  Detail & Related papers  (2024-11-06T17:09:28Z)
• Toward a physically motivated notion of Gaussian complexity geometry [0.0]
  We present a construction of a geometric notion of circuit complexity for Gaussian states. We show how to account for time-reversal symmetry breaking in measures of complexity. This establishes a first step towards building a quantitative, geometric notion of complexity.
  arXiv  Detail & Related papers  (2023-09-25T18:00:01Z)
• Fluctuations, uncertainty relations, and the geometry of quantum state manifolds [0.0]
  The complete quantum metric of a parametrized quantum system has a real part and a symplectic imaginary part. We show that for a mixed quantum-classical system both real and imaginary parts of the quantum metric contribute to the dynamics.
  arXiv  Detail & Related papers  (2023-09-07T10:31:59Z)
• Bounds on quantum evolution complexity via lattice cryptography [0.0]
  We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries.
  arXiv  Detail & Related papers  (2022-02-28T16:20:10Z)
• A Quantum Complexity Lowerbound from Differential Geometry [0.0]
  I apply the Bishop-Gromov bound to Nielsen's complexity geometry to prove lowerbounds on the quantum complexity of a typical unitary. For a broad class of penalty schedules, the typical complexity is shown to be exponentially large in the number of qubits. This method realizes the original vision of Nielsen, which was to apply the tools of differential geometry to study quantum complexity.
  arXiv  Detail & Related papers  (2021-12-10T18:28:01Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• 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)
• Local optimization on pure Gaussian state manifolds [63.76263875368856]
  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm. The method is based on notions of descent gradient attuned to the local geometry. We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
  arXiv  Detail & Related papers  (2020-09-24T18:00:36Z)
• 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)
• A refinement of Reznick's Positivstellensatz with applications to quantum information theory [72.8349503901712]
  In Hilbert's 17th problem Artin showed that any positive definite in several variables can be written as the quotient of two sums of squares. Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of the squared norm of the variables.
  arXiv  Detail & Related papers  (2019-09-04T11:46:26Z)

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.