48 research outputs found
Witnessed entanglement and the geometric measure of quantum discord
We establish relations between geometric quantum discord and entanglement
quantifiers obtained by means of optimal witness operators. In particular, we
prove a relation between negativity and geometric discord in the
Hilbert-Schmidt norm, which is slightly different from a previous conjectured
one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the
geometric discord with the trace norm, better bounds can be obtained. We
illustrate our results numerically.Comment: 8 pages + 3 figures. Revised version with erratum for PRA 86, 024302
(2012). Simplified proof that discord is bounded by entanglement in any nor
Viable entanglement detection of unknown mixed states in low dimensions
We explore procedures to detect entanglement of unknown mixed states, which
can be experimentally viable. The heart of the method is a hierarchy of simple
feasibility problems, which provides sufficient conditions to entanglement. Our
numerical investigations indicate that the entanglement is detected with a cost
which is much lower than full state tomography. The procedure is applicable to
both free and bound entanglement, and involves only single copy measurements.Comment: 8 pages, 9 figures, 4 table
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