We compute the quantum correlation (quantum discord (QD)) and the entanglement (EoF) between nearest neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EoF and other thermodynamic quantities, spotlight the critical points associated to quantum phase transitions (QPT) for this model even at finite T . This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen. Quantum phase transition (QPT) is a purely quantum process [1] occurring at absolute zero temperature (T = 0), where no thermal fluctuations exist and hence no classical phase transition is allowed to occur. QPT is caused by changing the system's Hamiltonian, such as an external magnetic field or the coupling constant. These quantities are generally known as the tuning parameter. As one changes the Hamiltonian one may reach a special point (critical point) where the ground state of the system suffers an abrupt change mapped to a macroscopic change in the system's properties. This change of phase is solely due to quantum fluctuations, which exist at T = 0 due to the Heisenberg uncertainty principle. This whole process is called QPT. The paramagnetic-ferromagnetic transition in some metals [2], the superconductor-insulator transition [3], and superfluid-Mott insulator transition [4] are remarkable examples of this sort of phase transition.In principle QPTs occur at T = 0, which is unattainable experimentally due to the third law of thermodynamics. Hence, one must work at very small T , as close as possible to the absolute zero, in order to detect a QPT. More precisely, one needs to work at regimes in which thermal fluctuations are insufficient to drive the system from its ground to excited states. In this scenario quantum fluctuations dominate and one is able to measure a QPT.So far the theoretical tools available to determine the critical points (CP) for a given Hamiltonian assume T = 0. For spin chains, for instance, the CPs are determined studying, as one varies the tuning parameter, the behavior of either its magnetization, or bipartite [5] and multipartite [6] entanglement, or its quantum correlation (QC) [7]. By investigating the extremal values of these quantities as well as the behavior of their first and second order derivatives one is able to spotlight the CP. However, the T = 0 assumption limits a direct connection between these theoretical "CP detectors" and experiment. Indeed, if thermal fluctuations are not small enough excited states become relevant and the tools developed so far cannot be employed to clearly indicate the CP.In this Letter we remove this limitation and present a theoretical tool that is able to clearly detect CPs for QPTs at finite T . We show that the behavior of strictly QCs [8] at finite T , as gi...

We investigate how quantum correlations (quantum discord (QD)) of a two-qubit one dimensional XYZ Heisenberg chain in thermal equilibrium depend on the temperature T of the bath and also on an external magnetic field B. We show that the behavior of thermal QD differs in many unexpected ways from thermal entanglement. For example, we show situations where QD increases with T when entanglement decreases, cases where QD increases with T even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite T. We also show that by properly tuning B or the interaction between the qubits we get non-zero QD for any T and we present a new effect not seen for entanglement, the "regrowth" of thermal QD.

A generalized teleportation protocol (GTP) for N qubits is presented, where the teleportation channels are non-maximally entangled and all the free parameters of the protocol are considered: Alice's measurement basis, her sets of acceptable results, and Bob's unitary operations. The full range of Fidelity (F ) of the teleported state and the Probability of Success (Psuc) to obtain a given fidelity are achieved by changing these free parameters. A channel efficiency bound is found, where one can determine how to divide it between F and Psuc. A one qubit formulation is presented and then expanded to N qubits. A proposed experimental setup that implements the GTP is given using linear optics.

We introduce a perturbative approach to solving the time dependent Schrödinger equation, named adiabatic perturbation theory (APT), whose zeroth order term is the quantum adiabatic approximation. The small parameter in the power series expansion of the time-dependent wave function is the inverse of the time it takes to drive the system's Hamiltonian from the initial to its final form. We review other standard perturbative and non-perturbative ways of going beyond the adiabatic approximation, extending and finding exact relations among them, and also compare the efficiency of those methods against the APT. Most importantly, we determine APT corrections to the Berry phase by use of the Aharonov-Anandan geometric phase. We then solve several time dependent problems allowing us to illustrate that the APT is the only perturbative method that gives the right corrections to the adiabatic approximation. Finally, we propose an experiment to measure the APT corrections to the Berry phase and show, for a particular spin-1/2 problem, that to first order in APT the geometric phase should be two and a half times the (adiabatic) Berry phase.

We explicitly show a protocol in which an arbitrary two qubit |φ = a|00 + b|01 + c|10 + d|11 is faithfully and deterministically teleported from Alice to Bob. We construct the 16 orthogonal generalized Bell states which can be used to teleport the two qubits. The local operations Bob must perform on his qubits in order to recover the teleported state is also constructed. They are restricted only to single qubit gates. This means that a CNOT gate is not necessary to complete the protocol. A generalization where N qubits is teleported is also shown. We define a generalized magic basis, which possesses interesting properties. These properties help us to suggest a generalized concurrence from which we construct a new measure of entanglement that has a clear physical interpretation: A multipartite state has maximum entanglement if it is a genuine quantum teleportation channel.

We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system's time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.

We investigate how the efficiency of the quantum teleportation protocol is affected when the qubits involved in the protocol are subjected to noise or decoherence. We study all types of noise usually encountered in real world implementations of quantum communication protocols, namely, the bit flip, phase flip (phase damping), depolarizing, and amplitude damping noise. Several realistic scenarios are studied in which a part or all of the qubits employed in the execution of the quantum teleportation protocol are subjected to the same or different types of noise. We find noise scenarios not yet known in which more noise or less entanglement lead to more efficiency. Furthermore, we show that if noise is unavoidable it is better to subject the qubits to different noise channels in order to obtain an increase in the efficiency of the protocol.

We use a Heisenberg spin-1/2 chain to investigate how chaos and localization may affect the entanglement of pairs of qubits. To measure how much entangled a pair is, we compute its concurrence, which is then analyzed in the delocalized/localized and in the chaotic/non-chaotic regimes. Our results indicate that chaos reduces entanglement and that entanglement decreases in the region of strong localization. In the transition region from a chaotic to a non-chaotic regime localization increases entanglement. We also show that entanglement is larger for strongly interacting qubits (nearest neighbors) than for weakly interacting qubits (next and next-next neighbors).Comment: 7 pages, 4 figures, RevTex4, Published versio