Quantum Correlations and Coherence in Spin-1 Heisenberg Chains

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.Comment: 8 pages. 5 figure

Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment

We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.Comment: 11 pages, 10 figure

Negativity and quantum discord in Davies environments

We investigate the time evolution of negativity and quantum discord for a pair of non-interacting qubits with one being weakly coupled to a decohering Davies--type Markovian environment. At initial time of preparation, the qubits are prepared in one of the maximally entangled pure Bell states. In the limiting case of pure decoherence (i.e. pure dephasing), both, the quantum discord and negativity decay to zero in the long time limit. In presence of a manifest dissipative dynamics, the entanglement negativity undergoes a sudden death at finite time while the quantum discord relaxes continuously to zero with increasing time. We find that in dephasing environments the decay of the negativity is more propitious with increasing time; in contrast, the evolving decay of the quantum discord proceeds weaker for dissipative environments. Particularly, the slowest decay of the quantum discord emerges when the energy relaxation time matches the dephasing time.Comment: submitted for publicatio

Measurement-induced geometric measures of correlations based on the trace distance for two-qubit X states

We apply the modified Brodutch and Modi method of constructing geometric measures of correlations to obtain analytical expressions for measurement-induced geometric classical and quantum correlations based on the trace distance for two-qubit X states. Moreover, we study continuity of the classical and quantum correlations for these states. In particular, we show that these correlations may not be continuous

Quantum Statistical Complexity Measure as a Signaling of Correlation Transitions

We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signaling function of quantum order–disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in correlation distributions. We apply our measure on two exactly solvable Hamiltonian models: the 1D-Quantum Ising Model (in the single-particle reduced state), and on Heisenberg XXZ spin-1/2 chain (in the two-particle reduced state). We analyze its behavior across quantum phase transitions for finite system sizes, as well as in the thermodynamic limit by using Bethe Ansatz technique