Related papers: Maximum-likelihood reconstruction of CP maps
Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that…
We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer…
The problem of extending the insights and techniques of categorical quantum mechanics to infinite-dimensional systems was considered in (Coecke and Heunen, 2016). In that work the $\mathrm{CP}^{\infty}$-construction, which recovers the…
We discuss an approach to the component separation of microwave, multi-frequency sky maps as those typically produced from Cosmic Microwave Background (CMB) Anisotropy data sets. The algorithm is based on the two step, parametric,…
Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the…
The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context we carry out a…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way [E. Woodhead et al., Phys. Rev. Research 2, 042028(R)(2020)], the problem of optimal…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
The Box--Cox transformation model has been widely applied for many years. The parametric version of this model assumes that the random error follows a parametric distribution, say the normal distribution, and estimates the model parameters…
We study methods of inducing metrics on unital completely positive maps by employing seminorms arising in noncommutative geometry. Our main approach relies on the development of an infinite-dimensional $C^*$-algebraic analogue of the…
Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
The maximum likelihood strategy to the estimation of group parameters allows to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results…
We study positive kernels on $X\times X$, where $X$ is a set equipped with an action of a group, and taking values in the set of $\mathcal A$-sesquilinear forms on a (not necessarily Hilbert) module over a $C^*$-algebra $\mathcal A$. These…
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose…
We demonstrate how insights gained from reformulating the problem of quantum teleportation into one of reversing quantum operations, and designing optimum completely positive maps for teleportation, can enable one to explore optimal…
In this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement when the original quantum state is known to be a member of some specified set. A suitable figure of merit for this…