206 research outputs found
Characterization and properties of weakly optimal entanglement witnesses
We present an analysis of the properties and characteristics of weakly
optimal entanglement witnesses, that is witnesses whose expectation value
vanishes on at least one product vector. Any weakly optimal entanglement
witness can be written as the form of ,
where is a non-negative number and is the identity
matrix. We show the relation between the weakly optimal witness and
the eigenvalues of the separable states . Further we give an
application of weakly optimal witnesses for constructing entanglement witnesses
in a larger Hilbert space by extending the result of [P. Badzi\c{a}g {\it et
al}, Phys. Rev. A {\bf 88}, 010301(R) (2013)], and we examine their geometric
properties.Comment: 13 pages, 2 figures, has been extensively redrafted and restructure
Structural physical approximations and entanglement witnesses
The structural physical approximation (SPA) to a positive map is considered
to be one of the most important method to detect entanglement in the real
physical world. We first show that an arbitrary entanglement witness (EW)
can be constructed from a separable density matrix in the form of
, where is a non-negative number and is
the identity matrix. Following the general form of EWs from separable states,
we show a sufficient condition and a sufficient and necessary condition in low
dimensions of that SPAs to positive maps do not define entanglement-breaking
channels. We show that either the SPA of an EW or the SPA of the partial
transposition of the EW in low dimensions is an entanglement-breaking channel.
We give sufficient conditions of violating the SPA conjecture [\emph{Phys. Rev.
A}{\bf 78,} 062105 (2008)]. Our results indicate that the SPA conjecture is
independent of whether or not positive maps are optimal.Comment: 7 pages, fixed some typos, thanks to the many comments received
Poly[[diaquahemi-μ4-oxalato-μ2-oxalato-praseodymium(III)] monohydrate]
In the title complex, {[Pr(C2O4)1.5(H2O)2]·H2O}n, the PrIII ion, which lies on a crystallographic inversion centre, is coordinated by seven O atoms from four oxalate ligands and two O atoms from two water ligands; further Pr—O coordination from tetradentate oxalate ligands forms a three-dimensional structure. The compound crystallized as a monohydrate, the water molecule occupying space in small voids and being secured by O—H⋯O hydrogen bonding as an acceptor from ligand water H atoms and as a donor to oxalate O-acceptor sites
Comfort-driven disparity adjustment for stereoscopic video
Pixel disparity—the offset of corresponding pixels between left and right views—is a crucial parameter in stereoscopic three-dimensional (S3D) video, as it determines the depth perceived by the human visual system (HVS). Unsuitable pixel disparity distribution throughout an S3D video may lead to visual discomfort. We present a unified and extensible stereoscopic video disparity adjustment framework which improves the viewing experience for an S3D video by keeping the perceived 3D appearance as unchanged as possible while minimizing discomfort. We first analyse disparity and motion attributes of S3D video in general, then derive a wide-ranging visual discomfort metric from existing perceptual comfort models. An objective function based on this metric is used as the basis of a hierarchical optimisation method to find a disparity mapping function for each input video frame. Warping-based disparity manipulation is then applied to the input video to generate the output video, using the desired disparity mappings as constraints. Our comfort metric takes into account disparity range, motion, and stereoscopic window violation; the framework could easily be extended to use further visual comfort models. We demonstrate the power of our approach using both animated cartoons and real S3D videos
Constructing all entanglement witnesses from density matrices
We demonstrate a general procedure to construct entanglement witnesses for
any entangled state. This procedure is based on the trace inequality and a
general form of entanglement witnesses, which is in the form , where is a density matrix, is a non-negative number
related to , and is the identity matrix. The general form of
entanglement witnesses is deduced from Choi-Jamio{\l}kowski isomorphism, that
can be reinterpreted as that all quantum states can be obtained by a maximally
quantum entangled state pass through certain completely positive maps.
Furthermore, we provide the necessary and sufficient condition of the
entanglement witness in operation, as well as in theory.Comment: 5 pages. Added the computing in detai
The Origin of Separable States and Separability Criteria from Entanglement-breaking Channels
In this paper, we show that an arbitrary separable state can be the output of
a certain entanglement-breaking channel corresponding exactly to the input of a
maximally entangled state. A necessary and sufficient separability criterion
and some sufficient separability criteria from entanglement-breaking channels
are given.Comment: EBCs with trace-preserving and EBCs without trace-preserving are
separately discusse
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