On Locality of Schmidt-Correlated States

We review some results on the equivalence of quantum states under local unitary transformations (LUT). In particular, the classification of two-qubit Schmidt correlated (SC) states under LUT is investigated. By presenting the standard form of quantum states under LUT, the sufficient and necessary conditions of whether two different SC states are local unitary equivalent are provided. The correlations of SC states are also discussed.Comment: 14 page

Revisiting the holographic dark energy in a non-flat universe: alternative model and cosmological parameter constraints

We propose an alternative model for the holographic dark energy in a non-flat universe. This new model differs from the previous one in that the IR length cutoff $L$ is taken to be exactly the event horizon size in a non-flat universe, which is more natural and theoretically/conceptually concordant with the model of holographic dark energy in a flat universe. We constrain the model using the recent observational data including the type Ia supernova data from SNLS3, the baryon acoustic oscillation data from 6dF, SDSS-DR7, BOSS-DR11, and WiggleZ, the cosmic microwave background data from Planck, and the Hubble constant measurement from HST. In particular, since some previous studies have shown that the color-luminosity parameter $\beta$ of supernovae is likely to vary during the cosmic evolution, we also consider such a case that $\beta$ in SNLS3 is time-varying in our data fitting. Compared to the constant $\beta$ case, the time-varying $\beta$ case reduces the value of $\chi^2$ by about 35 and results in that $\beta$ deviates from a constant at about 5$\sigma$ level, well consistent with the previous studies. For the parameter $c$ of the holographic dark energy, the constant $\beta$ fit gives $c=0.65\pm 0.05$ and the time-varying $\beta$ fit yields $c=0.72\pm 0.06$. In addition, an open universe is favored (at about 2$\sigma$) for the model by the current data.Comment: 8 pages, 4 figure

Unfolding Hidden Barriers by Active Enhanced Sampling

Collective variable (CV) or order parameter based enhanced sampling algorithms have achieved great success due to their ability to efficiently explore the rough potential energy landscapes of complex systems. However, the degeneracy of microscopic configurations, originating from the orthogonal space perpendicular to the CVs, is likely to shadow "hidden barriers" and greatly reduce the efficiency of CV-based sampling. Here we demonstrate that systematic machine learning CV, through enhanced sampling, can iteratively lift such degeneracies on the fly. We introduce an active learning scheme that consists of a parametric CV learner based on deep neural network and a CV-based enhanced sampler. Our active enhanced sampling (AES) algorithm is capable of identifying the least informative regions based on a historical sample, forming a positive feedback loop between the CV learner and sampler. This approach is able to globally preserve kinetic characteristics by incrementally enhancing both sample completeness and CV quality.Comment: 5 pages, 3 figure

A Note on State Decomposition Independent Local Invariants

We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations

Quantum state transfer from light to molecules via coherent two-color photo-association in an atomic Bose-Einstein condensate

By using a quantized input light, we theoretically revisit the coherent two-color photo-association process in an atomic Bose-Einstein condensate. Under the single-mode approximations, we show two interesting regimes of the light transmission and the molecular generation. The quantum state transfer from light to molecules is exhibited, without or with the depletion of trapped atoms.Comment: 1 figure, accepted by Eur.Phys.J.D on Dec.15,200