Misc,
Two qubits can be entangled in two distinct temperature regions
(May 2006)
Abstract
We present an example of a two-qubit Hamiltonian such that the
canonical-ensemble thermal state is entangled in two distinct temperature
regions. This example is in contrast to an expectation expressed in O. Osenda
and G. A. Raggio, Phys. Rev. A 72, 064102 (2005) and demonstrates that for
two-qubits where thermal entanglement is possible, the qualitative behavior of
entanglement as a function of temperature is not simply determined by the
ground-state entanglement. Furthermore, we prove a finite bound on the number
of possible entangled regions for two qubits, thus showing that arbitrarily
many transitions from entanglement to separability are not possible. We also
provide an elementary proof that the spectrum of the thermal state at a lower
temperature majorizes that at a higher temperature, for any Hamiltonian, and
use this result to show that only one entangled region is possible for the
special case of Bell-diagonal Hamiltonians.
