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.
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