arXiv subjects

A. R. Kuzmak

Publications and source records attributed to A. R. Kuzmak.

23 records · Page 2Linked to original sources

arXiv2017

Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution

Quantum evolution of a two-spin system with anisotropic Heisenberg Hamiltonian in the magnetic field is considered. We show that this evolution happens on some manifold with geometry depending on the ratio between the interaction couplings and on the initial state. The Fubini-Study metric of this manifold is calculated. The entanglement of the states belonging to this manifold is examined. Also we investigate similar problem for a two-spin system described by the Dzyaloshinsky-Moria Hamiltonian. The problem is solved using the fact that this Hamiltonian and the anisotropic Heisenberg Hamiltonian are linked by the unitary transformation.

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arXiv2015

Geometry of a two-spin quantum state in evolution

We study the quantum evolution of a two-spin system described by the isotropic Heisenberg Hamiltonian in the external magnetic field. It is shown that this evolution happens on a two-parametric closed manifold. The Fubini-Study metric of this manifold is obtained. It is found that this is the metric of the torus. The entanglement of the states which belong to this manifold is investigated.

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arXiv2015

The quantum brachistochrone problem for an arbitrary spin in a magnetic field

We consider quantum brachistochrone evolution for a spin-$s$ system on rotational manifolds. Such manifolds are determined by the rotation of the eigenstates of the operator of projection of spin-$s$ on some direction. The Fubini-Study metrics of these manifolds are those of spheres with radii dependent on the value of the spin and on the value of the spin projection. The conditions for optimal evolution of the spin-$s$ system on rotational manifolds are obtained.

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arXiv2014

Preparation of quantum states of two spin-$\frac{1}{2}$ particles in the form of the Schmidt decomposition

We consider a system of two spins that are coupled via an isotropic Heisenberg Hamiltonian. For the first time, a two-step method for the preparation of an arbitrary quantum state of two qubits in the form of the Schmidt decomposition is proposed. The simplified version of this method is applied to the physical system of an atom having with a nuclear spin $1/2$ and one valence electron. As an example, the preparation of two-spin quantum states in the $^{31}$P system is considered.

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arXiv2013

Quantum brachistochrone problem for two spins-1/2 with anisotropic Heisenberg interaction

We study the quantum brachistochrone evolution for a system of two spins-$\frac{1}{2}$ described by an anisotropic Heisenberg Hamiltonian without $zx$, $zy$ interacting couplings in magnetic field directed along the z-axis. This Hamiltonian realizes quantum evolution in two subspaces spanned by $\|\uparrow\uparrow\rangle$, $\|\downarrow\downarrow\rangle$ and $\|\uparrow\downarrow\rangle$, $\|\downarrow\uparrow\rangle$ separately and allows to consider the brachistochrone problem on each subspace separately. Using the evolution operator for this Hamiltonian we generate quantum gates, namely an entangler gate, SWAP gate, iSWAP gate et al.

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