Mixed-state quantum anomaly and multipartite entanglement

• URL: http://arxiv.org/abs/2401.17357v3
• Date: Wed, 26 Jun 2024 17:25:30 GMT
• Title: Mixed-state quantum anomaly and multipartite entanglement
• Authors: Leonardo A. Lessa, Meng Cheng, Chong Wang,
• Abstract summary: 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.
• Score: 8.070164241593814
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here we explore a surprising connection between mixed state entanglement and 't Hooft anomaly. More specifically, we consider lattice systems in $d$ space dimensions with anomalous symmetry $G$ where the anomaly is characterized by an invariant in the group cohomology $H^{d+2}(G,U(1))$. We show that any mixed state $\rho$ that is strongly symmetric under $G$, in the sense that $G\rho\propto\rho$, is necessarily $(d+2)$-nonseparable, i.e. is not the mixture of tensor products of $d+2$ states in the Hilbert space. Furthermore, such states cannot be prepared from any $(d+2)$-separable states using finite-depth local quantum channels, so the nonseparability is long-ranged in nature. We provide proof of these results in $d\leq1$, and plausibility arguments in $d>1$. The anomaly-nonseparability connection thus allows us to generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement. In particular, in $d=1$ we found an example of intrinsically mixed quantum phase, in the sense that states in this phase cannot be two-way connected to any pure state through finite-depth local quantum channels. We also briefly discuss mixed anomaly involving both strong and weak symmetries, including systems constrained by the Lieb-Schultz-Mattis type of anomaly.

Related papers

• Quantum Correlations in One Parameter Mixed Quantum States [0.0]
  We investigate the comparative dynamics of mixed states $(rhol,rhon,rhom)$ under the bipartite Ising Hamiltonian exposed by the external magnetic field.
  arXiv  Detail & Related papers  (2024-11-28T04:56:55Z)
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  The interplay between symmetry and topological properties plays a very important role in modern physics. How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• 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)
• Anomaly in open quantum systems and its implications on mixed-state quantum phases [6.356631694532754]
  We develop a systematic approach to characterize the 't Hooft anomaly in open quantum systems. By representing their symmetry transformation through superoperators, we incorporate them in a unified framework. We find that anomalies of bosonic systems are classified by $Hd+2(Ktimes G,U(1))/Hd+2(G,U(1))$ in $d$ spatial dimensions.
  arXiv  Detail & Related papers  (2024-03-21T16:34:37Z)
• Intrinsic Mixed-state Topological Order [4.41737598556146]
  We show that decoherence can give rise to new types of topological order. We construct concrete examples by proliferating fermionic anyons in the toric code via local quantum channels. The resulting mixed states retain long-range entanglement, which manifests in the nonzero topological entanglement negativity.
  arXiv  Detail & Related papers  (2023-07-25T18:34:10Z)
• Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations [17.209060627291315]
  We prove concentration for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [DPMRF22]; (ii) injective matrix product states, answering an open question from [DPMRF22]; (iii) output states of dense Hamiltonian evolution, i.e. states of the form $eiota H(p) cdots eiota H(1) |psirangle for any $n$-qubit product state $|psirangle$, where each $H(
  arXiv  Detail & Related papers  (2022-09-06T18:00:02Z)
• Non-zero momentum requires long-range entanglement [6.018940870331878]
  We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum. The statement can also be generalized to fermion systems.
  arXiv  Detail & Related papers  (2021-12-13T19:00:04Z)
• Canonical Quantum Coarse-Graining and Surfaces of Ignorance [0.0]
  We use negentropy to connect ignorance as measured by quantum information entropy and ignorance related to quantum coarse-graining. Our procedure reproduces features of Boltzmann's original coarse-graining by showing that the majority of phase space consists of states near or at equilibrium.
  arXiv  Detail & Related papers  (2021-11-15T15:23:38Z)
• 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)
• Constructions of $k$-uniform states from mixed orthogonal arrays [18.378398718548016]
  We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. We present two constructions of $2$-uniform states in heterogeneous systems. We show that some $k$-uniform bases can not be distinguished by local operations and classical communications.
  arXiv  Detail & Related papers  (2020-06-07T08:35:22Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.