相关论文: On PSI-complete and PSIR-complete measurements

The expectation value <O> of an arbitrary operator O can be obtained via a universal measuring apparatus that is independent of O, by changing only the data-processing of the outcomes. Such a ``universal detector'' performs a joint…

A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement…

The equilibrium conditions impose nontrivial geometrical constraints on the configurations that a two-dimensional foam can attain. In the first place, the three centers of the films that converge to a vertex have to be on a line, i.e. all…

We give necessary and sufficient conditions to specify vector bundles of conformal blocks for $\mathfrak{sl}_{2m}$ with rectangular weights which have ranks zero, one, and larger than one. First Chern classes of rank one bundles are shown…

We study the extreme points of the convex set $\mathcal{C}(\rho_1,\rho_2)$ of bipartite quantum states with fixed marginals $\rho_1$ and $\rho_2$. We construct extreme points in $(d,\,d+m)$ dimension, of rank $d+m$, matching the highest…

Generalized quantum measurements (POVMs or POMs) are important for optimally extracting information for quantum communication and computation. The standard realization via the Neumark extension requires extensive resources in the form of…

Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular…

We give necessary and sufficient conditions for the set of Neumark projections of a countable set of phase space observable to constitute a resolution of the identity, and we give a criteria for a phase space observable to be…

We obtain a polynomial upper bound in the finite-field version of the multidimensional polynomial Szemer\'{e}di theorem for distinct-degree polynomials. That is, if $P_1, ..., P_t$ are nonconstant integer polynomials of distinct degrees and…

We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…

Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on…

Edidin [3] proved a fundamental result in phase retrieval: Theorem: A family of orthogonal projections $\{P_i\}_{i=1}^m$ does phase retrieval in $\mathbb{R}^n$ if and only if for every $0\not= x\in \mathbb{R}^n$, the family…

In this paper we derive a necessary condition for finite element method (FEM) convergence in $H^1(\Omega)$ as well as generalize known sufficient conditions. We deal with the piecewise linear conforming FEM on triangular meshes for…

Complex projective t-designs, particularly SICs and full sets of MUBs, play an important role in quantum information. We introduce a generalization which we call conical t-designs. They include arbitrary rank symmetric informationally…

We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…

The construction of physically relevant low dimensional state models, and the design of appropriate measurements are key issues in tackling quantum state tomography for large dimensional systems. We consider the statistical problem of…

We present a proof-of-principle demonstration of a method to characterize \textit{any} pure spatial qudit of arbitrary dimension $d$, which is based on the classic phase shift interferometry technique. In the proposed scheme a total of only…

We study separability problem using general symmetric informationally complete measurements and propose separability criteria in $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}$ and…

The conditions for the existence of force-free non-relativistic translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria are investigated using general properties of the 1D VM equilibrium problem. As has been shown…

Measurement is the only part of a general quantum system that has yet to be characterized experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully…