1,929 research outputs found
Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution
We search for translationally invariant states of qubits on a ring that
maximize the nearest neighbor entanglement. This problem was initially studied
by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map
the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ
model. Using the exact Bethe ansatz solution in the limit of an infinite ring,
we prove the correctness of the assumption of O'Connor and Wootters that the
state of maximal entanglement does not have any pair of neighboring spins
``down'' (or, alternatively spins ``up''). For sufficiently small fixed
magnetization, however, the assumption does not hold: we identify the region of
magnetizations for which the states that maximize the nearest neighbor
entanglement necessarily contain pairs of neighboring spins ``down''.Comment: 10 pages, 4 figures; Eq. (45) and Fig. 3 corrected, no qualitative
change in conclusion
Entanglement, quantum phase transition and scaling in XXZ chain
Motivated by recent development in quantum entanglement, we study relations
among concurrence , SU(2) algebra, quantum phase transition and
correlation length at the zero temperature for the XXZ chain. We find that at
the SU(2) point, the ground state possess the maximum concurrence. When the
anisotropic parameter is deformed, however, its value decreases. Its
dependence on scales as in the XY metallic
phase and near the critical point (i.e. ) of the Ising-like
insulating phase. We also study the dependence of on the correlation length
, and show that it satisfies near the critical point. For
different size of the system, we show that there exists a universal scaling
function of with respect to the correlation length .Comment: 4 pages, 3 figures. to appear in Phys. Rev.
Maximizing nearest neighbour entanglement in finitely correlated qubit--chains
We consider translationally invariant states of an infinite one dimensional
chain of qubits or spin-1/2 particles. We maximize the entanglement shared by
nearest neighbours via a variational approach based on finitely correlated
states. We find an upper bound of nearest neighbour concurrence equal to
C=0.434095 which is 0.09% away from the bound C_W=0.434467 obtained by a
completely different procedure. The obtained state maximizing nearest neighbour
entanglement seems to approximate the maximally entangled mixed states (MEMS).
Further we investigate in detail several other properties of the so obtained
optimal state.Comment: 12 pages, 4 figures, 2nd version minor change
Entanglement in a simple quantum phase transition
What entanglement is present in naturally occurring physical systems at
thermal equilibrium? Most such systems are intractable and it is desirable to
study simple but realistic systems which can be solved. An example of such a
system is the 1D infinite-lattice anisotropic XY model. This model is exactly
solvable using the Jordan-Wigner transform, and it is possible to calculate the
two-site reduced density matrix for all pairs of sites. Using the two-site
density matrix, the entanglement of formation between any two sites is
calculated for all parameter values and temperatures. We also study the
entanglement in the transverse Ising model, a special case of the XY model,
which exhibits a quantum phase transition. It is found that the next-nearest
neighbour entanglement (though not the nearest-neighbour entanglement) is a
maximum at the critical point. Furthermore, we show that the critical point in
the transverse Ising model corresponds to a transition in the behaviour of the
entanglement between a single site and the remainder of the lattice.Comment: 14 pages, 7 eps figure
Long-distance entanglement and quantum teleportation in XX spin chains
Isotropic XX models of one-dimensional spin-1/2 chains are investigated with
the aim to elucidate the formal structure and the physical properties that
allow these systems to act as channels for long-distance, high-fidelity quantum
teleportation. We introduce two types of models: I) open, dimerized XX chains,
and II) open XX chains with small end bonds. For both models we obtain the
exact expressions for the end-to-end correlations and the scaling of the energy
gap with the length of the chain. We determine the end-to-end concurrence and
show that model I) supports true long-distance entanglement at zero
temperature, while model II) supports {\it ``quasi long-distance''}
entanglement that slowly falls off with the size of the chain. Due to the
different scalings of the gaps, respectively exponential for model I) and
algebraic in model II), we demonstrate that the latter allows for efficient
qubit teleportation with high fidelity in sufficiently long chains even at
moderately low temperatures.Comment: 9 pages, 6 figure
Entanglement and transport through correlated quantum dot
We study quantum entanglement in a single-level quantum dot in the
linear-response regime. The results show, that the maximal quantum value of the
conductance 2e^2/h not always match the maximal entanglement. The pairwise
entanglement between the quantum dot and the nearest atom of the lead is also
analyzed by utilizing the Wootters formula for charge and spin degrees of
freedom separately. The coexistence of zero concurrence and the maximal
conductance is observed for low values of the dot-lead hybridization. Moreover,
the pairwise concurrence vanish simultaneously for charge and spin degrees of
freedom, when the Kondo resonance is present in the system. The values of a
Kondo temperature, corresponding to the zero-concurrence boundary, are also
provided.Comment: Presented on the International Conference "Nanoelectronics '06", 7-8
January 2006, Lancaster, U
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