Gaussian quantum information over general quantum kinematical systems I: Gaussian states

• URL: http://arxiv.org/abs/2204.08162v1
• Date: Mon, 18 Apr 2022 04:51:29 GMT
• Title: Gaussian quantum information over general quantum kinematical systems I: Gaussian states
• Authors: Cedric Beny, Jason Crann, Hun Hee Lee, Sang-Jun Park and Sang-Gyun Youn
• Abstract summary: We develop a theory of Gaussian states over general quantum kinematical systems with finitely many degrees of freedom. Our characterization reveals a topological obstruction to Gaussian state entanglement when we decompose the quantum kinematical system into the Euclidean part. We also examine angle-number systems with phase space $mathbbTntimesmathbbZn$ and fermionic/hardcore bosonic systems with phase space $mathbbZ2n$.
• Score: 1.266953082426463
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We develop a theory of Gaussian states over general quantum kinematical systems with finitely many degrees of freedom. The underlying phase space is described by a locally compact abelian (LCA) group $G$ with a symplectic structure determined by a 2-cocycle on $G$. We use the concept of Gaussian distributions on LCA groups in the sense of Bernstein to define Gaussian states and completely characterize Gaussian states over 2-regular LCA groups of the form $G= F\times\hat{F}$ endowed with a canonical normalized 2-cocycle. This covers, in particular, the case of $n$-bosonic modes, $n$-qudit systems with odd $d\ge 3$, and $p$-adic quantum systems. Our characterization reveals a topological obstruction to Gaussian state entanglement when we decompose the quantum kinematical system into the Euclidean part and the remaining part (whose phase space admits a compact open subgroup). We then generalize the discrete Hudson theorem \cite{Gro} to the case of totally disconnected 2-regular LCA groups. We also examine angle-number systems with phase space $\mathbb{T}^n\times\mathbb{Z}^n$ and fermionic/hard-core bosonic systems with phase space $\mathbb{Z}^{2n}_2$ (which are not 2-regular), and completely characterize their Gaussian states.

Related papers

• Representation theory of Gaussian unitary transformations for bosonic and fermionic systems [0.0]
  We analyze the behavior of the sign ambiguity that one needs to deal with when moving between the groups of the symplectic and special annihilation group. We show how we can efficiently describe group multiplications in the double cover without the need of going to a faithful representation on an exponentially large or even infinite-dimensional space.
  arXiv  Detail & Related papers  (2024-09-18T01:22:38Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• 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)
• Mixed-state quantum anomaly and multipartite entanglement [8.070164241593814]
  We show a surprising connection between mixed state entanglement and 't Hooft anomaly. We generate examples of mixed states with nontrivial long-ranged multipartite entanglement. We also briefly discuss mixed anomaly involving both strong and weak symmetries.
  arXiv  Detail & Related papers  (2024-01-30T19:00:02Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• On quantum tomography on locally compact groups [0.0]
  We introduce quantum tomography on locally compact Abelian groups $G$. We provide three examples in which $G=mathbb R$ (the optical tomography), $G=mathbb Z_n$ (corresponding to measurements in mutually unbiased bases) and $G=mathbb T$ (the tomography of the phase) As an application we have calculated the quantum tomogram for the output states of quantum Weyl channels.
  arXiv  Detail & Related papers  (2022-01-16T13:48:22Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)
• Bosonic and fermionic Gaussian states from K\"ahler structures [0.0]
  We show that bosonic and fermionic Gaussian states can be uniquely characterized by their linear complex structure $J$. We apply these methods to the study of entanglement and complexity, (B) dynamics of stable systems, (C) dynamics of driven systems.
  arXiv  Detail & Related papers  (2020-10-29T12:21:47Z)
• Spectral statistics in constrained many-body quantum chaotic systems [0.0]
  We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints. In particular, we analytically argue that in a system of length $L$ that conserves the $mth$ multipole moment, $t_mathrmTh$ scales subdiffusively as $L2(m+1)$.
  arXiv  Detail & Related papers  (2020-09-24T17:59:57Z)

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.