Related papers: Optimal reconstruction systems for erasures and fo…
Given a finite sequence of vectors $\mathcal F_0$ in $\C^d$ we describe the spectral and geometrical structure of optimal completions of $\mathcal F_0$ obtained by adding a finite sequence of vectors with prescribed norms, where optimality…
This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame coefficients. We address two distinct erasure scenarios and…
Error occurs in data transmission process when some data are missing at the time of reconstruction. Finding the best dual frame or a dual pair that minimizes the reconstruction error when erasure occurs,is a deep-rooted problem in frame…
The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…
We introduce an extension of the convex potentials for finite frames (e.g. the frame potential defined by Benedetto and Fickus) in the framework of Bessel sequences of integer translates of finite sequences in $L^2(\R^k)$. We show that…
We investigate the precision limits and optimal protocols for sensing single qubit signals in the presence of erasure noise. We study a hierarchy of precision limits achievable with metrological strategies of differing complexity, and…
We consider the problem of developing a method to reconstruct a potential $q$ from the partial data Dirichlet-to-Neumann map for the Schr\"odinger equation $(-\Delta_g+q)u=0$ on a fixed admissible manifold $(M,g)$. If the part of the…
In this paper we study the fusion frame potential, that is a generalization of the Benedetto-Fickus (vectorial) frame potential to the finite-dimensional fusion frame setting. The structure of local and global minimizers of this potential…
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $\mathcal F$ we describe the spectral and geometrical structure of optimal completions of $\mathcal F$ by a finite family of vectors with…
We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
Erasure qubits offer a promising avenue toward reducing the overhead of quantum error correction (QEC) protocols. However, they require additional operations, such as erasure checks, that may add extra noise and increase runtime of QEC…
The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here, we resolve a…
A natural criticism of the optimal protocol of the irreversible work found for weakly driven processes is its experimental difficulty in being implementable due to its singular part. In this work, I explore the possibility of taking its…
Let $I\subseteq \Bbb N$ be a finite or infinite set and let ${(x_n)_{n\in I}}$ be a frame for a separable Hilbert space $\mathcal{H}$. Consider transmission of a signal $h\in\mathcal{H}$ where a finite subset $(\langle h,x_n\rangle)_{n\in…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
The quantum internet holds promise for performing quantum communication, such as quantum teleportation and quantum key distribution, freely between any parties all over the globe. For such a quantum internet protocol, a general fundamental…
We consider finite frames with high redundancy so that if half the terms transmitted from the sender are randomly deleted during transmission, then on average, the receiver can still recover the signal to within a high level of accuracy.…
For an initially well designed but imperfect quantum information system, the process matrix is almost sparse in an appropriate basis. Existing theory and associated computational methods (L1-norm minimization) for reconstructing sparse…
In this paper we introduce a new probabilistic model for optimizing erasures occurring in data transmission using Parseval frames and a sequence of Bernoulli random variables associated to the channels of the transmission. We establish…