Thiago. R. de Oliveira

arXiv2013

Geometric quantum discord through the Schatten 1-norm

It has recently been pointed out that the geometric quantum discord, as defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum correlations, since it may increase under local reversible operations on the unmeasured subsystem. Here, we revisit the geometric discord by considering general Schatten p-norms, explicitly showing that the 1-norm is the only p-norm able to define a consistent quantum correlation measure. In addition, by restricting the optimization to the tetrahedron of two-qubit Bell-diagonal states, we provide an analytical expression for the 1-norm geometric discord, which turns out to be equivalent to the negativity of quantumness. We illustrate the measure by analyzing its monotonicity properties.

quant-ph↗

arXiv2008

Scaling of entanglement support for Matrix Product States

The power of matrix product states to describe infinite-size translational-invariant critical spin chains is investigated. At criticality, the accuracy with which they describe ground state properties of a system is limited by the size $χ$ of the matrices that form the approximation. This limitation is quantified in terms of the scaling of the half-chain entanglement entropy. In the case of the quantum Ising model, we find $S \sim {1/6}\log χ$ with high precision. This result can be understood as the emergence of an effective finite correlation length $ξ_χ$ ruling of all the scaling properties in the system. We produce five extra pieces of evidence for this finite-$χ$ scaling, namely, the scaling of the correlation length, the scaling of magnetization, the shift of the critical point, and the scaling of the entanglement entropy for a finite block of spins. All our computations are consistent with a scaling relation of the form $ξ_χ\sim χ^κ$, with $κ=2$ for the Ising model. In the case of the Heisenberg model, we find similar results with the value $κ\sim 1.37$. We also show how finite-$χ$ scaling allow to extract critical exponents. These results are obtained using the infinite time evolved block decimation algorithm which works in the thermodynamical limit and are verified to agree with density matrix renormalization group results.

cond-mat.stat-mech↗