Related papers: Unital Kadison-Schwarz Maps
Entanglement is not only the most intriguing feature of quantum mechanics, but also a key resource in quantum information science. The entanglement content of random pure quantum states is almost maximal; such states find applications in…
Higher-dimensional entanglement is a valuable resource for several quantum information processing tasks, and is often characterized by the Schmidt number and specific classes of entangled states beyond qubit-qubit and qubit-qutrit systems.…
Multipartite quantum entanglement, as a core quantum resource, is fundamental to the advancement of quantum science and technology. In multipartite quantum systems, there are two kinds of quantum entanglement: $k$-nonseparability and…
We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements…
Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criteria is a powerful tool for detection of entangled states in…
A class of unital qubit maps displaying diagonal unitary and orthogonal symmetries is analyzed. Such maps already found a lot applications in quantum information theory. We provide a complete characterization of this class of maps showing…
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement…
Quantum entanglement is known as a unique quantum feature that cannot be obtained by classical physics. Over the last several decades, however, such an understanding on quantum entanglement might have confined us in a limited world of weird…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
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…
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…
Entanglement constitutes a key characteristic feature of quantum matter. Its detection, however, still faces major challenges. In this letter, we formulate a framework for probing entanglement based on machine learning techniques. The…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
Entanglement of states and Complete Positivity of maps are concepts that have achieved physical importance with the recent growth of quantum information science. They are however mathematically relevant whenever tensor products of complex…
Entanglement plays a central role in quantum information processing, indicating the non-local correlation of quantum matters. However, few effective ways are known to detect the amount of entanglement of an unknown quantum state. In this…
We study k Kadison Schwarz (k KS) mappings on matrix algebras and derive explicit conditions ensuring the k KS property for two classes of maps parameterized by a single k-positive map.
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…