Symmetric States and Dynamics of Three Quantum Bits
- URL: http://arxiv.org/abs/2111.07208v1
- Date: Sat, 13 Nov 2021 23:32:15 GMT
- Title: Symmetric States and Dynamics of Three Quantum Bits
- Authors: Francesca Albertini and Domenico D'Alessandro
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The unitary group acting on the Hilbert space of three quantum bits admits a
Lie subgroup, of elements which permute with the symmetric group of
permutations. Under the action of such Lie subgroup, the Hilbert space splits
into three invariant subspaces of dimensions 4, 2 and 2 respectively, each
corresponding to an irreducible representation of su(2). The subspace of
dimension 4 is uniquely determined and corresponds to states that are
themselves invariant under the action of the symmetric group. This is the so
called symmetric sector.
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 parametrize all the possible invariant
two-dimensional subspaces and extend the previous analysis to these subspaces
as well. 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. For such set up, we solve a control
theoretic problem which consists of driving a separable state to a state with
maximal distributed entanglement.
Related papers
- Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators.
We find conditions for their strong continuity and establish properties of their generators.
arXiv Detail & Related papers (2024-06-15T17:39:32Z) - 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) - 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) - Deformed Symmetry Structures and Quantum Many-body Scar Subspaces [12.416248333306237]
A quantum many-body scar system usually contains a special non-thermal subspace decoupled from the rest of the Hilbert space.
We propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars.
arXiv Detail & Related papers (2021-08-17T18:00:02Z) - Role of symmetry in quantum search via continuous-time quantum walk [0.0]
We discuss how the symmetries of the graphs are related to the existence of such an invariant subspace.
This discussion also suggests that all the symmetries are used up in the invariant subspace and the asymmetric part of the Hamiltonian is very important for the purpose of quantum search.
arXiv Detail & Related papers (2021-06-15T19:55:37Z) - Geometric quantification of multiparty entanglement through
orthogonality of vectors [0.0]
We show that post-measurement vectors can yield non-identical set of maximally entangled states.
We discuss the trade-off between the local properties namely predictability and coherence with the global property.
arXiv Detail & Related papers (2021-03-06T08:28:07Z) - Complete entropic inequalities for quantum Markov chains [17.21921346541951]
We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality.
We also establish the first general approximateization property of relative entropy.
arXiv Detail & Related papers (2021-02-08T11:47:37Z) - Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles.
Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature.
We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
arXiv Detail & Related papers (2020-11-06T19:00:07Z) - Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide.
For open boundary condition, we find exotic topological bound-pair edge states with radiative losses.
By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
arXiv Detail & Related papers (2020-02-24T04:44:12Z)
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.