Related papers: 3-Uniform states and orthogonal arrays
A $k$-pairable $n$-qubit state is a resource state that allows Local Operations and Classical Communication (LOCC) protocols to generate EPR-pairs among any $k$-disjoint pairs of the $n$ qubits. Bravyi et al. introduced a family of…
Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence…
$k$-Uniform states are fundamental to quantum information and computing, with applications in multipartite entanglement and quantum error-correcting codes (QECCs). Prior work has primarily focused on constructing exact $k$-uniform states or…
Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability…
We review 28 uniform partitions of 3-space in order to find out which of them have graphs (skeletons) embeddable isometrically (or with scale 2) into some cubic lattice ${\bf Z}_n$. We also consider some relatives of those 28 partitions,…
We describe a (3,3)-homogeneous orthomodular posets for some cardinality of their sets of atoms. We examine a state space and a set of two-valued states of such logics. Particular homogeneous OMPs with exactly k pure states (k=1,...,7,…
The existence of $k$-uniform states has been a widely studied problem due to their applications in several quantum information tasks and their close relation to combinatorial objects like Latin squares and orthogonal arrays. With the…
A pure quantum state of $n$ parties associated with the Hilbert space $\CC^{d_1}\otimes \CC^{d_2}\otimes\cdots\otimes \CC^{d_n}$ is called $k$-uniform if all the reductions to $k$-parties are maximally mixed. The $n$ partite system is…
We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence…
Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in…
We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of non-generic three-qubit mixed states. It is shown that two…
In this paper we present a modified version of the proof given Jing-Yang-Zhao's paper titled "Local Unitary Equivalence of Quantum States and Simultaneous Orthogonal Equivalence," which established the correspondance between local unitary…
We experimentally test the recently predicted anisotropic invariance properties of pure three-qubit states, via generation and measurement of polarisation-path entangled three-qubit states. These properties do not require aligned reference…
The Schr\"odinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This…
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to…
We construct a canonical form for pure states in $\bwe^3(\bC^6)$, the three-fermion system with six single particle states, under local unitary (LU) transformations, i.e., the unitary group $\Un(6)$. We also construct a minimal set of…
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally…
This paper considers a class of qubit channels for which three states are always sufficient to achieve the Holevo capacity. For these channels it is known that there are cases where two orthogonal states are sufficient, two non-orthogonal…
Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…