Affine maps of density matrices

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system; an affine map can be replaced by a linear map, and a linear map can be replaced by an affine map. There may be significant advantage in using an affine map. The linear map is generally not completely positive, but the linear part of an equivalent affine map can be chosen to be completely positive and related in the simplest possible way to the unitary Hamiltonian evolution in the larger system.Comment: 4 pages, title changed, sentence added, reference update

Remote sensing observatory validation of surface soil moisture using Advanced Microwave Scanning Radiometer E, Common Land Model, and ground based data: Case study in SMEX03 Little River Region, Georgia, U.S.

Optimal soil moisture estimation may be characterized by intercomparisons among remotely sensed measurements, ground‐based measurements, and land surface models. In this study, we compared soil moisture from Advanced Microwave Scanning Radiometer E (AMSR‐E), ground‐based measurements, and a Soil‐Vegetation‐Atmosphere Transfer (SVAT) model for the Soil Moisture Experiments in 2003 (SMEX03) Little River region, Georgia. The Common Land Model (CLM) reasonably replicated soil moisture patterns in dry down and wetting after rainfall though it had modest wet biases (0.001–0.054 m3/m3) as compared to AMSR‐E and ground data. While the AMSR‐E average soil moisture agreed well with the other data sources, it had extremely low temporal variability, especially during the growing season from May to October. The comparison results showed that highest mean absolute error (MAE) and root mean squared error (RMSE) were 0.054 and 0.059 m3/m3 for short and long periods, respectively. Even if CLM and AMSR‐E had complementary strengths, low MAE (0.018–0.054 m3/m3) and RMSE (0.023–0.059 m3/m3) soil moisture errors for CLM and soil moisture low biases (0.003–0.031 m3/m3) for AMSR‐E, care should be taken prior to employing AMSR‐E retrieved soil moisture products directly for hydrological application due to its failure to replicate temporal variability. AMSR‐E error characteristics identified in this study should be used to guide enhancement of retrieval algorithms and improve satellite observations for hydrological sciences

Necessary and sufficient conditions for bipartite entanglement

Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary Hermitian operators, which makes them useful for applications in experiments. The needed optimization procedure is based on a separability eigenvalue problem, whose analytical solutions are derived for a special class of projection operators. For general Hermitian operators, a numerical implementation of entanglement tests is proposed. It is also shown how to identify bound entangled states with positive partial transposition.Comment: 7 pages, 2 figur

A method to find quantum noiseless subsystems

We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in terms of the superoperator perspective, or the algebraic noise commutant formalism. As an application, we propose a method for finding all such subspaces and subsystems for arbitrary quantum operations. We suggest that this work brings the fundamental passive technique for error correction in quantum computing an important step closer to practical realization.Comment: 5 pages, to appear in Physical Review Letter

On multipartite invariant states I. Unitary symmetry

We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states: separability criteria and multi-PPT conditions.Comment: 9 pages; slight correction

Identifying the Higgs Spin and Parity in Decays to Z Pairs

Higgs decays to Z boson pairs may be exploited to determine spin and parity of the Higgs boson, a method complementary to spin-parity measurements in Higgs-strahlung. For a Higgs mass above the on-shell ZZ decay threshold, a model-independent analysis can be performed, but only by making use of additional angular correlation effects in gluon-gluon fusion at the LHC and gamma-gamma fusion at linear colliders. In the intermediate mass range, in which the Higgs boson decays into pairs of real and virtual Z bosons, threshold effects and angular correlations, parallel to Higgs-strahlung, may be adopted to determine spin and parity, though high event rates will be required for the analysis in practice.Comment: 14 pages, 2 postscript figure

Partial scaling transform of multiqubit states as a criterion of separability

The partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of quantum states. The transform contains partial transposition as a special case. The scaling transform corresponds to partial time scaling of subsystem (or partial Planck's constant scaling) which was used to formulate recently separability criterion for continous variables.A measure of entanglement which is a generalization of negativity measure is introduced being based on tomographic probability description of spin states.Comment: 16 pages, 5 figures, submitted to J. Phys. A: Math. Ge