相关论文: Coefficient Quantization for Frames in Banach Spac…

Let (e_i) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a `finite alphabet'. We investigate several…

Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…

We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…

Composite quantum systems can be decomposed into subsystems in many different inequivalent ways. We call a particular decomposition a meronomic reference frame for the system. We apply the ideas of quantum reference frames to characterize…

Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to…

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…

Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in…

In this paper, we propose to define the concept of family of local atoms and then we generalize this concept to the atomic system for operator in Banach spaces by using semi-inner product. We also give a characterization of atomic systems…

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…

Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…

We study properties of representing and absolutely representing systems of subspaces in Banach spaces. We also present sufficient conditions for the system of subspaces to be a representing system of subspaces.

In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…

Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…

It is demonstrated that the so-called "unavoidable quantum anomalies" can be avoided in the farmework of a special non-linear quantization scheme. A simple example is discussed in detail.

The notion of retro Banach frame with the help of b-linear functional in n-Banach spaces is being presented. Some properties related to the construction of new retro Banach frame in n-Banach space have been studied. In n-Banach spaces, some…

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…

In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…

In this article, we introduce the concept of weakly uniquely stationary representations. This framework enables us to investigate the complementability of closed subspaces within the context of continuous cohomology with coeffcients in…

We outline the scheme for quantization of classical Banach space results associated with some prototypes of dynamical maps and describe the quantization of correlations as well. A relation between these two areas is discussed.

In this paper we present a unified algebraic framework to discuss the reduction of classical and quantum systems. The underlying algebraic structure is a Lie-Jordan algebra supplemented, in the quantum case, with a Banach structure. We…