Teleportation via thermally entangled state of a two-qubit Heisenberg XX chain

We find that quantum teleportation, using the thermally entangled state of two-qubit Heisenberg XX chain as a resource, with fidelity better than any classical communication protocol is possible. However, a thermal state with a greater amount of thermal entanglement does not necessarily yield better fidelity. It depends on the amount of mixing between the separable state and maximally entangled state in the spectra of the twoqubit Heisenberg XX model. The linearity of quantum mechanics allows building of superposition states of composite system SAB that cannot be written as products of states of each subsystem (SA and SB). Such states are called entangled. States which are not entangled are referred to as separable states. An entangled composite system gives rise to nonlocal correlation between its subsystems that does not exist classically. This nonlocal property enables the uses of local quantum operations and classical communication to transmit an unknown state |ψ〉 via a shared pair of entangled particles, with fidelity better than any classical communication protocol [1, 2, 3]. The standard teleportation protocol P0 uses Bell measurements and Pauli rotations. Standard teleportation with an arbitrary mixed state resource ρAB is equivalent to a generalized depolarizng channel ΛP0(ρAB) with probabilites given by the maximally entangled components of the resource [4]. The fidelity for P0 and ρAB is defined by averaging 〈ψ| [ΛP0 (ρAB) |ψ〉〈ψ|] |ψ〉 over all possible |ψ〉. Quantum teleportation can thus serve as an operational test of the presence and strength of entanglement in ρAB. Recently, the presence of entanglement in condensed-matter systems at finite temperatures has been investigated by a number of authors (see, e.g., [5] and references therein). The state of a typical condensed-matter system at thermal equilibrium (temperature T ) is ρ = e−βH/Z where H is the Hamiltonian, Z = tre−βH is the partition function, and β = 1/kT where k is Boltzmann’s constant. The entanglement associated with the thermal state ρ is referred to as