Deformations of the symmetric subspace of qubit chains

• URL: http://arxiv.org/abs/2503.23554v2
• Date: Tue, 01 Apr 2025 15:59:29 GMT
• Title: Deformations of the symmetric subspace of qubit chains
• Authors: Angel Ballesteros, Ivan Gutierrez-Sagredo, Jose de Ramon, J. Javier Relancio,
• Abstract summary: We present deformations of the symmetric subspace as deformations of a group structure $mathcalU_q(mathfraksu(2))$.<n>We see that deformations of the symmetric subspace correspond to local deformations of the inner product of each spin, in such a way that departure from symmetry can be encoded in a position-dependent inner product.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The symmetric subspace of multi-qubit systems, that is, the space of states invariant under permutations, is commonly encountered in applications in the context of quantum information and communication theory. It is known that the symmetric subspace can be described in terms of irreducible representations of the group $SU(2)$, whose representation spaces form a basis of symmetric states, the so-called Dicke states. In this work, we present deformations of the symmetric subspace as deformations of this group structure, which are promoted to a quantum group $\mathcal{U}_q(\mathfrak{su}(2))$. We see that deformations of the symmetric subspace obtained in this manner correspond to local deformations of the inner product of each spin, in such a way that departure from symmetry can be encoded in a position-dependent inner product. The consequences and possible extensions of these results are also discussed.

Related papers

• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbour (between unit cells)<n>Our invariant is invariant under unitary and similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks [43.88179780450706]
  We investigate the impact of weight space permutation symmetries on variational inference. We devise a symmetric symmetrization mechanism for constructing permutation invariant variational posteriors. We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective.
  arXiv  Detail & Related papers  (2024-08-10T09:06:34Z)
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections [0.0]
  Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way.<n>In this paper, we systematically study the gauging of finite Abelian modulated symmetries in $1+1$ dimensions.
  arXiv  Detail & Related papers  (2024-06-18T18:00:00Z)
• Multipartite entanglement in the diagonal symmetric subspace [39.58317527488534]
  For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$.<n>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)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Entanglement of Quantum States which are Zero on the Symmetric Sector [0.0]
  We consider a quantum system of n qudits and the Clebsch-Gordan decomposition of the associated Hilbert space. We prove that any separable state must have a nonzero component on the symmetric sector. We identify a class of entanglement witnesses for these systems.
  arXiv  Detail & Related papers  (2023-11-28T22:48:24Z)
• Theory of Quantum Circuits with Abelian Symmetries [0.0]
  Generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry.<n>We show that while the locality of interactions still imposes additional constraints on realizable unitaries, certain restrictions do not apply to circuits with Abelian symmetries.<n>This result suggests that global non-Abelian symmetries may affect the thermalization of quantum systems in ways not possible under Abelian symmetries.
  arXiv  Detail & Related papers  (2023-02-24T05:47:13Z)
• Classifying phases protected by matrix product operator symmetries using matrix product states [0.0]
  We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry.
  arXiv  Detail & Related papers  (2022-03-23T17:25:30Z)
• 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)
• Symmetric States and Dynamics of Three Quantum Bits [0.0]
  We provide an analysis of pure states in the symmetric sector of three quantum bits for what concerns their entanglement properties, separability criteria and dynamics. We propose a physical set up for the states and dynamics we study which consists of a symmetric network of three spin 1/2 particles under a common driving electro-magnetic field.
  arXiv  Detail & Related papers  (2021-11-13T23:32:15Z)
• Quantum Relativity of Subsystems [58.720142291102135]
  We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
  arXiv  Detail & Related papers  (2021-03-01T19:00:01Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)

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.