Symmetry-Resolved Relative Entropy of Random States

• URL: http://arxiv.org/abs/2411.01491v1
• Date: Sun, 03 Nov 2024 09:16:24 GMT
• Title: Symmetry-Resolved Relative Entropy of Random States
• Authors: Mostafa Ghasemi,
• Abstract summary: We calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior.
• Score: 0.0
• License:
• Abstract: We use large-$N$ diagrammatic techniques to calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. These methods are specifically designed for symmetric sectors, allowing us to determine the relative entropy for random states exhibiting $U(1)$ symmetry. This calculation serves as a measure of distinguishability within the symmetry sectors of random states. Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior. Furthermore, we derive the symmetry-resolved Page curve. These results deepen our understanding of the properties of these random states.

Related papers

• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Multipartite entanglement in the diagonal symmetric subspace [41.94295877935867]
  For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$. We present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension.
  arXiv  Detail & Related papers  (2024-03-08T12:06:16Z)
• Asymmetry activation and its relation to coherence under permutation operation [53.64687146666141]
  A Dicke state and its decohered state are invariant for permutation. When another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation.
  arXiv  Detail & Related papers  (2023-11-17T03:33:40Z)
• A quantum tug of war between randomness and symmetries on homogeneous spaces [0.0]
  We consider states as $H$-equivalent if related by a symmetry transformation characterized by the group $H$. We introduce the Haar measure on the homogeneous space $mathbbU/H$, characterizing true randomness for $H$-equivalent systems.
  arXiv  Detail & Related papers  (2023-09-11T06:06:31Z)
• Asymptotic Equipartition Theorems in von Neumann algebras [24.1712628013996]
  We show that the smooth max entropy of i.i.d. states on a von Neumann algebra has an rate given by the quantum relative entropy. Our AEP not only applies to states, but also to quantum channels with appropriate restrictions.
  arXiv  Detail & Related papers  (2022-12-30T13:42:35Z)
• Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
  We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
  arXiv  Detail & Related papers  (2022-08-05T16:35:24Z)
• 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)
• Symmetry protected entanglement in random mixed states [0.0]
  We study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $mathbbZ_N$ and $U(1)$ symmetry groups.
  arXiv  Detail & Related papers  (2021-11-30T19:00:07Z)
• Symmetry Breaking in Symmetric Tensor Decomposition [44.181747424363245]
  We consider the nonsymmetry problem associated with computing the points rank decomposition of symmetric tensors. We show that critical points the loss function is detected by standard methods.
  arXiv  Detail & Related papers  (2021-03-10T18:11:22Z)
• Discrimination of symmetric states in operational probabilistic theory [2.030567625639093]
  In quantum theory, if a state set has a certain symmetry, there exists a minimum-error measurement having the same type of symmetry. We show that it also holds in OPTs, i.e., for a symmetric state set, there exists a minimum-error measurement that has the same type of symmetry. It is also shown that this result can be utilized to optimize over a restricted class of measurements, such as sequential or separable measurements.
  arXiv  Detail & Related papers  (2020-12-27T01:34:06Z)
• Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks [2.735801286587347]
  We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many symmetry-relevant scientific questions into simple optimization problems. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry-breaking input to deform a square into a rectangle and to generate octahedra tilting patterns in perovskites.
  arXiv  Detail & Related papers  (2020-07-04T17:24:21Z)

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.