Related papers: Maximum-likelihood reconstruction of CP maps
Positive maps are useful for detecting entanglement in quantum information theory. Any entangled state can be detected by some positive map. In this paper, the relation between positive block matrices and completely positive…
In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best,…
Positivity or the stronger notion of complete positivity, and contextuality are central properties of quantum dynamics. In this work, we demonstrate that a physical unitary-universe dilation model could be employed to characterize the…
An alternative, geometrical proof of a known theorem concerning the decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has been presented. The premise of the proof is the identification of positive maps with operators…
We give a criterion for a positive mapping on the space of operators on a Hilbert space to be indecomposable. We show that this criterion can be applied to two families of positive maps. These families of maps can then be used to form…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These…
We investigate the evolution of open quantum systems in the presence of initial correlations with an environment. Here the standard formalism of describing evolution by completely positive trace preserving (CPTP) quantum operations can fail…
The time evolution of an initially uncorrelated system is governed by a completely positive (CP) map. More generally, the system may contain initial (quantum) correlations with an environment, in which case the system evolves according to a…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We…
The notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity. An upper bound is derived for this quantity, and for several classes of maps (including CQ, QC and…
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements…
We establish explicit means via which natural dilations of completely positive (CP) maps can be constructed \`a la Kraus's IInd representation theorem. To obtain this, we rely on the Choi-Jamio{\l}kowski correspondence and develop a…
Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…
We present optimal and minimal measurements on identical copies of an unknown state of a qubit when the quality of measuring strategies is quantified with the gain of information (Kullback of probability distributions). We also show that…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
This work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator…