Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states

• URL: http://arxiv.org/abs/2204.09586v2
• Date: Mon, 8 Aug 2022 01:55:51 GMT
• Title: Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states
• Authors: K. Anjali, I. Reena, Sudha, B. G. Divyamani, H. S. Karthik, K. S. Mallesh and A. R. Usha Devi
• Abstract summary: We show that the pure entangled three-qubit states exhibit distinct geometric representation in terms of a spheroid inscribed within the Bloch sphere. We provide detailed analysis of the SLOCC canonical forms of the reduced two-qubit states extracted from entangled three-qubit pure symmetric states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that the pure entangled three-qubit symmetric states which are inequivalent under stochastic local operations and classcial communication (SLOCC) exhibit distinct geometric representation in terms of a spheroid inscribed within the Bloch sphere. We provide detailed analysis of the SLOCC canonical forms of the reduced two-qubit states extracted from entangled three-qubit pure symmetric states. Based on the Lorentz canonical forms of these states we arrive at two different geometrical representations: (i) a prolate spheroid centered at the origin of the Bloch sphere -- with longest semiaxis along the z-direction (symmetry axis of the spheroid) equal to 1 -- in the case of pure permutation symmetric three-qubit states constructed from 3 distinct spinors and (ii) a spheroid centered at (0,0,1/2) inside the Bloch sphere, with fixed semiaxes lengths (1/sqrt{2}, 1/sqrt{2}, 1/2) when the three-qubit pure state is constructed via symmetrization of 2 distinct spinors.

Related papers

• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order [17.38734393793605]
  We propose a new class of phases, termed the double ASPT phase, which emerges from a nontrivial extension of these two orders. This new phase is absent from prior studies and cannot exist in conventional closed systems.
  arXiv  Detail & Related papers  (2024-10-17T16:36:53Z)
• Wigner's Theorem for stabilizer states and quantum designs [0.6374763930914523]
  We describe the symmetry group of the stabilizer polytope for any number $n$ of systems and any prime local dimension $d$. In the qubit case, the symmetry group coincides with the linear and anti-linear Clifford operations. We extend an observation of Heinrich and Gross and show that the symmetries of fairly general sets of Hermitian operators are constrained by certain moments.
  arXiv  Detail & Related papers  (2024-05-27T18:00:13Z)
• Conformal geometry from entanglement [14.735587711294299]
  We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system. We show that stationarity of $mathfrakc_mathrmtot$ is equivalent to a vector fixed-point equation involving $eta$, making our assumption locally checkable.
  arXiv  Detail & Related papers  (2024-04-04T18:00:03Z)
• 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)
• 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)
• Lorentz canoncial forms of two-qubit states [0.0]
  The Bloch sphere provides an elegant way of visualizing a qubit. We show a detailed mathematical analysis of the real-matrix parametrization and associated geometric picturization of arbitrary two-qubit states.
  arXiv  Detail & Related papers  (2024-02-14T15:44:34Z)
• Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering [0.0]
  The steering ellipsoids corresponding to the two-qubit subsystems of permutation symmetric $N$-qubit states is analysed here. We construct and analyze the geometric features of the canonical steering ellipsoids corresponding to pure permutation symmetric $N$-qubit states with two distinct spinors.
  arXiv  Detail & Related papers  (2023-01-01T19:46:21Z)
• Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states [0.0]
  The quantum steering ellipsoids inscribed inside the Bloch sphere offer an elegant visualization of two-qubit states shared between Alice and Bob. The steering ellipsoids are shown to be effective in capturing quantum correlation properties, such as monogamy. We provide detailed analysis of the canonical forms and the associated steering ellipsoids of the reduced twoqubit states extracted from entangled three-qubit pure symmetric states.
  arXiv  Detail & Related papers  (2022-08-05T07:36:27Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• General superposition states associated to the rotational and inversion symmetries in the phase space [0.0]
  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.
  arXiv  Detail & Related papers  (2020-04-06T13:10:34Z)

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.