60 citations · 557 across the 47 of their papers we have counts for
43 papers · 1 filter
Local geometry for Schmidt number witnesses
Young-Hoon Kiem, Seung-Hyeok Kye
Suppose that is the face of the convex set of all bi-partite states which consists of states with ranges contained in a subspace . For generic subspaces w…
Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses
Kyung Hoon Han, Seung-Hyeok Kye
We consider the compact convex set of all bi-partite states of Schmidt number less than or equal to , together with that of -blockpositive matrices of trace one, which play t…
Global locations of Schmidt number witnesses
Kyung Hoon Han, Seung-Hyeok Kye
We investigate global locations of Schmidt number witnesses which are outside of the convex set of all bipartite states. Their locations are classified by interiors of faces of the…
Choi matrices revisited. III
Kyung Hoon Han, Seung-Hyeok Kye
We look for all linear isomorphisms from the mapping spaces onto the tensor products of matrices which send -superpositive maps onto unnormalized bi-partite states of Schmidt nu…
Choi matrices revisited. II
Kyung Hoon Han, Seung-Hyeok Kye
In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do…
Exposedness of elementary positive maps between matrix algebras
Seung-Hyeok Kye
The positive linear maps $\ad_s$ which send matrices to play important roles in quantum information theory as well as matrix theory. It was proved by Marciniak [Linear…
Compositions and tensor products of linear maps between matrix algebras
Seung-Hyeok Kye
In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement…
There exist infinitely many kinds of partial separability/entanglement
Kil-Chan Ha, Kyung Hoon Han, Seung-Hyeok Kye
In tri-partite systems, there are three basic biseparability, -, - and - biseparability according to bipartitions of local systems. We begin with three convex…
Polytope structures for Greenberger-Horne-Zeilinger diagonal states
Kyung Hoon Han, Seung-Hyeok Kye
We explore the polytope structures for genuine entanglement, biseparability, full biseparability and Bell inequality of multi-qubit GHZ diagonal states. We first show that bisepara…
Criteria for partial entanglement of three qubit states arising from distributive rules
Kyung Hoon Han, Seung-Hyeok Kye
It is known that the partial entanglement/separability violates distributive rules with respect to the operations of taking convex hull and intersection. In this note, we give crit…
Partial separability/entanglement violates distributive rules
Kyung Hoon Han, Seung-Hyeok Kye, Szilárd Szalay
We found three qubit Greenberger-Horne-Zeilinger diagonal states which tells us that the partial separability of three qubit states violates the distributive rules with respect to…
On the convex cones arising from classifications of partial entanglement in the three qubit system
Kyung Hoon Han, Seung-Hyeok Kye
In order to classify partial entanglement of multi-partite states, it is natural to consider the convex hulls, intersections and differences of basic convex cones obtained from par…
Entangled edge states of corank one with positive partial transposes
Jinwon Choi, Young-Hoon Kiem, Seung-Hyeok Kye
We construct a parameterized family of PPT (positive partial transpose) states of corank one for each . With a suitable choice of parameters, we show that they…
Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification
Kyung Hoon Han, Seung-Hyeok Kye
We construct seven kinds of three-qubit biseparable states to show that every class of biseparable states in the partial separability classification proposed by Szalay and Kökényes…
Three qubit separable states of length ten with unique decompositions
Seung-Hyeok Kye
We construct one parameter families of three qubit separable states with length ten, which is strictly greater than the whole dimension eight. These states are located on the bound…
Separability of multi-qubit states in terms of diagonal and anti-diagonal entries
Kil-Chan Ha, Kyung Hoon Han, Seung-Hyeok Kye
We give separability criteria for general multi-qubit states in terms of diagonal and anti-diagonal entries. We define two numbers which are obtained from diagonal and anti-diagona…
Separability criterion for three-qubit states with a four dimensional norm
Lin Chen, Kyung Hoon Han, Seung-Hyeok Kye
We give a separability criterion for three qubit states in terms of diagonal and anti-diagonal entries. This gives us a complete characterization of separability when all the entri…
The role of phases in detecting three-qubit entanglement
Kyung Hoon Han, Seung-Hyeok Kye
We propose separability criteria for three-qubit states in terms of diagonal and anti-diagonal entries to detect entanglement with positive partial transposes. We report that the p…
Separability of three qubit Greenberger-Horne-Zeilinger diagonal states
Kyung Hoon Han, Seung-Hyeok Kye
We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the…
Construction of three qubit genuine entanglement with bi-partite positive partial transposes
Kil-Chan Ha, Seung-Hyeok Kye
We construct tri-qubit genuinely entangled states which have positive partial transposes with respect to bi-partition of systems. These examples disprove a conjecture [L. Novo, T.…
Construction of multi-qubit optimal genuine entanglement witnesses
Kyung Hoon Han, Seung-Hyeok Kye
We interpret multi-partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them. We apply this result to multi-qubit {\sf X}-shaped Hermitian…
Various notions of positivity for bi-linear maps and applications to tri-partite entanglement
Kyung Hoon Han, Seung-Hyeok Kye
We consider bi-linear analogues of -positivity for linear maps. The dual objects of these notions can be described in terms of Schimdt ranks for tri-tensor products and Schmidt…
Three-qubit entanglement witnesses with the full spanning properties
Seung-Hyeok Kye
We construct three-qubit entanglement witnesses with the properties that all the partial transposes have the spanning properties. These witnesses determine faces for separable stat…
Multi-partite separable states with unique decompositions and construction of three qubit entanglement with positive partial transpose
Kil-Chan Ha, Seung-Hyeok Kye
We investigate conditions on a finite set of multi-partite product vectors for which separable states with corresponding product states have unique decomposition, and show that thi…