General superposition states associated to the rotational and inversion symmetries in the phase space

• URL: http://arxiv.org/abs/2004.02645v1
• Date: Mon, 6 Apr 2020 13:10:34 GMT
• Title: General superposition states associated to the rotational and inversion symmetries in the phase space
• Authors: Julio A L\'opez-Sald\'ivar
• Abstract summary: It is shown that the resulting states form an $n$-dimensional set of states which can lead to the finite representation of specific systems. The presence of nonclassical properties in these states as subpoissonian photon statistics is addressed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The general quantum superposition states containing the irreducible representation of the $n$-dimensional groups associated to the rotational symmetry of the $n$-sided regular polygon i.e. the cyclic group ($C_n$ ) and the rotational and inversion symmetries of the polygon, i.e. the dihedral group ($D_n$ ) are defined and studied. It is shown that the resulting states form an $n$-dimensional orthogonal set of states which can lead to the finite representation of specific systems. The correspondence between the symmetric states and the renormalized states, resulting from the selective erasure of photon numbers from an arbitrary, noninvariant initial state, is also established. As an example, the general cyclic Gaussian states are presented. The presence of nonclassical properties in these states as subpoissonian photon statistics is addressed. Also, their use in the calculation of physical quantities as the entanglement in a bipartite system is discussed.

Related papers

• Crystalline invariants of fractional Chern insulators [6.267386954898001]
  We show how ground state expectation values of partial rotations can be used to extract crystalline invariants. For the topological orders we consider, we show that the Hall conductivity, filling fraction, and partial rotation invariants fully characterize the system.
  arXiv  Detail & Related papers  (2024-05-27T17:59:59Z)
• Non-abelian symmetry-resolved entanglement entropy [1.433758865948252]
  We introduce a framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. We derive exact formulas for the average and the variance of the typical entanglement entropy for an ensemble of random pure states with fixed non-abelian charges. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry.
  arXiv  Detail & Related papers  (2024-05-01T16:06:48Z)
• 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)
• 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)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• 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)
• Representing and Learning Functions Invariant Under Crystallographic Groups [18.6870237776672]
  Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. We derive linear and nonlinear representations of functions that are (1) smooth and (2) invariant under such a group. We show that such a basis exists for each crystallographic group, that it is orthonormal in the relevant $L$ space, and recover the standard Fourier basis as a special case for pure shift groups.
  arXiv  Detail & Related papers  (2023-06-08T15:02:04Z)
• Symplectic tomographic probability distribution of crystallized Schr\"odinger cat states [1.2891210250935143]
  We study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides. We obtain the Wigner functions and tomographic probability distributions determining the density matrices of the states.
  arXiv  Detail & Related papers  (2022-03-15T11:03:47Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Classification of fractional quantum Hall states with spatial symmetries [0.0]
  Fractional quantum Hall (FQH) states are examples of symmetry-enriched topological states (SETs) In this paper we develop a theory of symmetry-protected topological invariants for FQH states with spatial symmetries.
  arXiv  Detail & Related papers  (2020-12-21T19:00:00Z)
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry [0.0]
  We develop a theory of symmetry-protected quantized invariants for topological phases defined on a lattice. We show how discrete rotational and translational symmetry fractionalization can be characterized by a discrete spin vector. The fractionally quantized charge polarization, which is non-trivial only on a lattice with $2$, $3$, and $4$-fold rotation symmetry, implies a fractional charge bound to lattice dislocations.
  arXiv  Detail & Related papers  (2020-05-20T18:00:05Z)

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.