Beyond islands: A free probabilistic approach

• URL: http://arxiv.org/abs/2209.10546v2
• Date: Fri, 23 Dec 2022 09:24:45 GMT
• Title: Beyond islands: A free probabilistic approach
• Authors: Jinzhao Wang
• Abstract summary: We show that the replica gravitational path is integrally matching the free multiplicative convolution between the spectra of the gravitational sector and the matter sector. The convolution formula computes the radiation entropy accurately even in cases when the island formula fails to apply.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give a free probabilistic proposal to compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model where the gravitational path integral can be implemented with full control. We observe that the replica trick gravitational path integral is combinatorially matching the free multiplicative convolution between the spectra of the gravitational sector and the matter sector respectively. The convolution formula computes the radiation entropy accurately even in cases when the island formula fails to apply. It also helps to justify this gravitational replica trick as a soluble Hausdorff moment problem. We then work out how the free convolution formula can be evaluated using free harmonic analysis, which also gives a new free probabilistic treatment of resolving the separable sample covariance matrix spectrum. The free convolution formula suggests that the quantum information encoded in competing quantum extremal surfaces can be modelled as free random variables in a finite von Neumann algebra. Using the close tie between free probability and random matrix theory, we show that the PSSY model can be described as a random matrix model that is essentially a generalization of Page's model. It is then manifest that the island formula is only applicable when the convolution factorizes in regimes characterized by the one-shot entropies. We further show that the convolution formula can be reorganized to a generalized entropy formula in terms of the relative entropy.

Related papers

• Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach [49.1574468325115]
  We introduce a method for reconstructing the corresponding Lindbaldian master equation given any target NESS. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. We illustrate the method in different systems, ranging from bosonic Gaussian to dissipative-driven collective spins.
  arXiv  Detail & Related papers  (2024-08-09T19:00:18Z)
• Closed-form solutions for the Salpeter equation [41.94295877935867]
  We study the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent problem, namely the B"aumer equation. This B"aumera corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy for small times and Gaussian diffusion for large times.
  arXiv  Detail & Related papers  (2024-06-26T15:52:39Z)
• Equivalence of dynamics of disordered quantum ensembles and semi-infinite lattices [44.99833362998488]
  We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice. This mapping provides a geometric interpretation on the loss of coherence when averaging over the ensemble and allows computation of the exact dynamics of the entire disordered ensemble in a single simulation.
  arXiv  Detail & Related papers  (2024-06-25T18:13:38Z)
• Tensor product random matrix theory [39.58317527488534]
  We introduce a real-time field theory approach to the evolution of correlated quantum systems. We describe the full range of such crossover dynamics, from initial product states to a maximum entropy ergodic state.
  arXiv  Detail & Related papers  (2024-04-16T21:40:57Z)
• Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process [0.0]
  Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We derive exact formulae for its mutual information between different subsystems in the steady state and show that it satisfies a volume law. Surprisingly, the QSSEP entanglement properties only depend on data related to its transport properties and we suspect that such a relation might hold for more general mesoscopic systems.
  arXiv  Detail & Related papers  (2023-04-21T14:37:14Z)
• Towards Entanglement Entropy of Random Large-N Theories [0.0]
  We use the replica approach and the notion of shifted Matsubara frequency to compute von Neumann and R'enyi entanglement entropies. We demonstrate the flexibility of the method by applying it to examples of a two-site problem in presence of decoherence.
  arXiv  Detail & Related papers  (2023-03-03T18:21:54Z)
• 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)
• Page curves and typical entanglement in linear optics [0.0]
  We study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We prove various results on the typicality of entanglement as measured by the R'enyi-2 entropy. Our main make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries.
  arXiv  Detail & Related papers  (2022-09-14T18:00:03Z)
• Symmetry-resolved Page curves [0.0]
  We study a natural extension in the presence of a conservation law and introduce the symmetry-resolved Page curves. We derive explicit analytic formulae for two important statistical ensembles with a $U(1)$-symmetry.
  arXiv  Detail & Related papers  (2022-06-10T13:22:14Z)
• 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)
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians [0.0]
  In integrable models, the volume-law coefficient depends on the subsystem fraction. We show that the average entanglement entropy of eigenstates of the power-law random banded matrix model is close but not the same as the result for quadratic models.
  arXiv  Detail & Related papers  (2020-06-19T18:01:15Z)

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.