Project 3: Entanglement in Mesospin Systems
3.3. Theoretical Analysis of Entanglement in Interacting Spin Systems
At present quantum computing is largely conceived as a low-temperature process,
because thermal randomization tends to destroy quantum coherence. Finite-temperature
quantum-computing effects have remained a difficult challenge. Exploiting entanglement
effects in mesoscopic spin systems is of crucial importance for future finite-temperature
quantum computing. In a recent paper [1], Lagmago Kamta and Starace have shown
that entanglement of a two-qubit Heisenberg XY chain having anisotropic interactions
can be produced at any finite temperature by applying a suitably strong magnetic
field directed along the z-axis. However, the relativistic smallness of Bohr's
magneton, µB/kB = 0.672 K/T, means that laboratory-scale
magnetic fields limit the temperature range to a few K. For example, a temperature
of 4.2 K corresponds to a magnetic field of 6.25 T, which is three times the
magnetization of a strong iron-core electromagnet, so that superconducting magnets
are required. The exploitation of level splittings due to magnetocrystalline
anisotropy, which is a key aspect of the present research, is an interesting
alternative to magnetic fields.
The entanglement problem becomes highly complicated if three or more spins are
involved. Efforts at entangling more than a pair of qubits are in their beginning
stages. In the past, quantum studies of mesoscopic spin structures have attracted
comparatively little attention. Quantum effects in magnetic nanostructures are
often treated on a 'micromagnetic' level, parameterizing for example the interatomic
exchange in terms of an exchange stiffness. This approach is meaningful when
the number of spins is sufficiently large to ensure a continuum-type averaging
over quantum states, but it is unable to address specific quantum-mechanical
problems.
A main aim of the planned theoretical research of Skomski is to identify the
low-lying quantum states for the above-mentioned experimental mesostructures
and to calculate their entanglement. Exchange coupling between two mesoscopic
spin blocks—or between substructures in specifically structured single
magnets—yields a variety of entangled and nonentangled quantum states,
in analogy to systems consisting of two interacting S = 1/2 spins. A second
aim of our theoretical research is to investigate the dynamics of entangled
and nonentangled states. This is necessary, for example, to gauge the decoherence
time, i.e., the time during which quantum coherence is maintained. A modest
initial effort will be devoted to examining also the effects of interactions
among three or more spins on the pairwise entanglement of the spins as a function
of time.
[1] G. Lagmago Kamta and A. F. Starace, “Anisotropy and Magnetic Field
Effects on the Entanglement of a Two Qubit Heisenberg XY Chain,” Phys.
Rev. Lett. 88, 107901 (2002).