On quantum non-signalling boxes

A classical non-signalling (or causal) box is an operation on classical bipartite input with classical bipartite output such that no signal can be sent from a party to the other through the use of the box. The quantum counterpart of such boxes, i.e. completely positive trace-preserving maps on bipartite states, though studied in literature, have been investigated less intensively than classical boxes. We present here some results and remarks about such maps. In particular, we analyze: the relations among properties as causality, non-locality and entanglement; the connection between causal and entanglement breaking maps; the characterization of causal maps in terms of the classification of states with fixed reductions. We also provide new proofs of the fact that every non-product unitary transformation is not causal, as well as for the equivalence of the so-called semicausality and semilocalizability properties.Comment: 18 pages, 7 figures, revtex

Blob-B-Gone: a lightweight framework for removing blob artifacts from 2D/3D MINFLUX single-particle tracking data

In this study, we introduce Blob-B-Gone, a lightweight framework to computationally differentiate and eventually remove dense isotropic localization accumulations (blobs) caused by artifactually immobilized particles in MINFLUX single-particle tracking (SPT) measurements. This approach uses purely geometrical features extracted from MINFLUX-detected single-particle trajectories, which are treated as point clouds of localizations. Employing k-means++ clustering, we perform single-shot separation of the feature space to rapidly extract blobs from the dataset without the need for training. We automatically annotate the resulting sub-sets and, finally, evaluate our results by means of principal component analysis (PCA), highlighting a clear separation in the feature space. We demonstrate our approach using two- and three-dimensional simulations of freely diffusing particles and blob artifacts based on parameters extracted from hand-labeled MINFLUX tracking data of fixed 23-nm bead samples and two-dimensional diffusing quantum dots on model lipid membranes. Applying Blob-B-Gone, we achieve a clear distinction between blob-like and other trajectories, represented in F1 scores of 0.998 (2D) and 1.0 (3D) as well as 0.995 (balanced) and 0.994 (imbalanced). This framework can be straightforwardly applied to similar situations, where discerning between blob and elongated time traces is desirable. Given a number of localizations sufficient to express geometric features, the method can operate on any generic point clouds presented to it, regardless of its origin

The Necessary and Sufficient Conditions of Separability for Multipartite Pure States

In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a necessary condition for a local unitary equivalence class for a bipartite system in terms of the determinant of the matrix of amplitudes and explore a variance as a measure of entanglement for multipartite pure states.Comment: Submitted to PRL in Sep. 2004, the paper No is LV9637. Submitted to SIAM on computing, in Jan., 2005, the paper No. is SICOMP 44687. Under reviewing no

Distinguishing multi-partite states by local measurements

We analyze the distinguishability norm on the states of a multi-partite system, defined by local measurements. Concretely, we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent to a multi-partite generalisation of the non-commutative 2-norm (aka Hilbert-Schmidt norm): in comparing the two, the constants of domination depend only on the number of parties but not on the Hilbert spaces dimensions. We discuss implications of this result on the corresponding norms for the class of all measurements implementable by local operations and classical communication (LOCC), and in particular on the leading order optimality of multi-party data hiding schemes.Comment: 18 pages, 6 figures, 1 unreferenced referenc

Управління трудовим потенціалом при створенні інноваційної продукції

Super-resolution microscopy (SRM) bypasses the diffraction limit, a physical barrier that restricts the optical resolution to roughly 250 nm and was previously thought to be impenetrable. SRM techniques allow the visualization of subcellular organization with unprecedented detail, but also confront biologists with the challenge of selecting the best-suited approach for their particular research question. Here, we provide guidance on how to use SRM techniques advantageously for investigating cellular structures and dynamics to promote new discoveries

Semicausal operations are semilocalizable

We prove a conjecture by DiVincenzo, which in the terminology of Preskill et al. [quant-ph/0102043] states that ``semicausal operations are semilocalizable''. That is, we show that any operation on the combined system of Alice and Bob, which does not allow Bob to send messages to Alice, can be represented as an operation by Alice, transmitting a quantum particle to Bob, and a local operation by Bob. The proof is based on the uniqueness of the Stinespring representation for a completely positive map. We sketch some of the problems in transferring these concepts to the context of relativistic quantum field theory.Comment: 4 pages, 1 figure, revte

Coverage-dependent adsorption sites in the K/Ru(0001) system: a low-energy electron-diffraction analysis

The two ordered phases p(2 × 2) at a coverage θ = 0.25 and (√3 × √3)R30° at θ = 0.33 of potassium adsorbed on Ru(0001) were analyzed by use of low-energy electron-diffraction (LEED). In the (√3 × √3)R30° phase, the K atoms occupy threefold hcp sites, while in the p(2 × 2) phase the fcc site is favoured. In both phases, the K hard-sphere radii are nearly the same and close to the covalent Pauling radius