Related papers: Classification of the separable maps which preserv…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…
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…
We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space $\cal{H}$, of any number of parties. Restricting consideration to measurements that act only on…
A new class of positive maps is introduced. It interpolates between positive and completely positive maps. It is shown that this class gives rise to a new characterization of entangled states. Additionally, it provides a refinement of the…
We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite…
It is well known that the number of entanglement classes in SLOCC (stochastic local operations and classical communication) classifications increases with the number of qubits and is already infinite for four qubits. Bearing in mind the…
The transformations of $W$-type entangled states by using local operations assisted with classical communication are investigated. For this purpose, a parametrization of the $W$-type states which remains invariant under local unitary…
We study the problem of distinguishing maximally entangled quantum states by using local operations and classical communication (LOCC). A question of fundamental interest is whether any three maximally entangled states in…
We derive a sufficient condition for a set of pure states, each entangled in two remote $N$-dimensional systems, to be transformable to $k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local operations and classical…
We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of…
The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert…
We exhibit a two-parameter family of bipartite mixed states $\rho_{bc}$, in a $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in $2\otimes…
We investigate the extent to which two particles can be maximally entangled when they are also similarly entangled with other particles on a complete graph, focusing on Werner, isotropic, and Brauer states. To address this, we formulate and…
We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent…
Given a PPT state $A=\sum_{i=1}^nA_i\otimes B_i \in M_k\otimes M_k$ and a vector $v\in\Im(A)\subset\mathbb{C}^k\otimes\mathbb{C}^k$ with tensor rank $k$, we provide an algorithm that checks whether the positive map $G_A:M_k\rightarrow M_k$,…
It is shown that while entanglement remains a significant factor in discriminating a set of mutually orthogonal entangled states perfectly by local operations and classical communication (LOCC), entanglement content is not. In particular,…
For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning…
The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different…
Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on…
In this work, we investigate the existence of a factorization for a unital completely positive map, between non-commutative probability space which do not change the expectation values of the events. These maps are called in literature…