Related papers: A new class of states with positive partial transp…
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…
Entanglement is a powerful resource for processing quantum information. In this context pure, maximally entangled states have received considerable attention. In the case of bipartite qubit-systems the four orthonormal Bell-states are of…
With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties…
In this thesis there are two topics: On the entangling capacity, in terms of negativity, of quantum operations, and on the supremum of negativity for symmetric Gaussian states. Positive partial transposition (PPT) states are an important…
We study the equivalence of quantum states under local unitary transformations by using the singular value decomposition. A complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed…
We consider bipartite quantum state discrimination using positive-partial-transpose measurements and show that minimum-error discrimination by positive-partial-transpose measurements is closely related to entanglement witness. By using the…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
Many alternative approaches to construct quantum channels with large entangling capacity were proposed in the past decade, resulting in multiple isolated gates. In this work, we put forward a novel one, inspired by convolution, which…
The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and the local projections are a fundamental operation in quantum physics. We investigate the relation between the Schmidt numbers of bipartite…
The study of entanglement properties of multi-qubit states that are invariant under permutations of qubits is motivated by potential applications in quantum computing, quantum communication, and quantum metrology. In this work, we…
We introduce a class of bipartite entangled continuous variable states that are positive under partial transposition operation, i.e., PPT bound entangled. These states are based on realistic preparation procedures in optical systems, being…
We introduce a 3-parameter class of maps acting on a bipartite system that are a natural generalisation of the depolarizing channel (and include it as a special case). Then, we find the exact regions of the parameter space that…
We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of…
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…
We construct multipartite entangled states with underlying W-type structure satisfying positive partial transpose (PPT) condition under any (N-1)|1 partition. Then we show how to distill N-partite secure key form the states using two…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
Necessary and sufficient observable conditions for the nonnegativity of all partial transpositions of multi-mode quantum states are derived. The result is a hierarchy of inequalities for minors in terms of moments of the given state.…
We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local…
Gram matrix approach to an entanglement analysis of pure states describing $(d,\infty)$ -- quantum systems is being introduced. In particular, maximally entangled states are described as those having a special forms of the corresponding…
Stochastic and bistochastic matrices providing positive maps for spin states (for qudits) are shown to form semigroups with dense intersection with the Lie groups $IGL(n, \mathbb{R})$ and $GL(n, \mathbb{R})$ respectively. The density matrix…