相关论文: On the stratifications of 2-qubits X-state space

For each of the groups $G = O(2), SU(2), U(2)$, we compute the integral and $\mathbb{F}_2$-cohomology rings of $B_\text{com} G$ (the classifying space for commutativity of $G$), the action of the Steenrod algebra on the mod 2 cohomology,…

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space-time dimension d<=4 is investigated. For that purpose, a description of orbit types in terms of…

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…

We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…

An intriguing correspondence between four-qubit systems and simple singularity of type $D_4$ is established. We first consider an algebraic variety $X$ of separable states within the projective Hilbert space…

Within the new description of the polarization structure of quantum light (given in Part I) some types of generalized coherent states related to the polarization SU(2) group are examined. With their help we give a quasiclassical description…

We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, W- and GHZ-states. These classes are successively embedded into each other. We show that contrary to pure W-type states,…

In the first half of this article, we review the Steinberg theory for double flag varieties for symmetric pairs. For a special case of the symmetric space of type AIII, we will consider $ X = GL_{2n}/P_{(n,n)} \times GL_n / B_n^+ \times…

We describe an explicit basis for the $\operatorname{SU}(2)$-invariant space of the exterior power $\wedge_{2k} \mathbb{C}^{2m}$ via the combinatorics of plane partitions. In quantum chemistry, this is the space of spin adapted quantum…

We first reconsider the mathematical background of superqubit theory and describe important peculiarities of superspaces and supermatrices which are usually out of attention. Then we study states in super Hilbert spaces using…

Let M be the set of mixed states and S the set of separable states of the two-qubit system, and G = SU(2) x SU(2) the group of local unitary transformations (ignoring the overall phase factor). We compute the multigraded Poincare series for…

The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times2\times4$ and $2\times2\times2\times4$ UPBs of size eight by using the existing…

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in space-time dimension d<=4 is presented. The method is based on the…

We determine the spaces of states of the two-dimensional $O(n)$ and $Q$-state Potts models with generic parameters $n,Q\in \mathbb{C}$ as representations of their known symmetry algebras. While the relevant representations of the conformal…

Except for a few special states, computing quantum discord remains a complicated optimization process. In this paper we present analytical solutions for computing quantum discord of the most general class of X-states and the criteria for…

The discussions in the present paper arise from exploring intrinsically the structure nature of the quantum $n$-space. A kind of braided category $\Cal {GB}$ of $\La$-graded $\th$-commutative associative algebras over a field $k$ is…

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…

We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For…

Computing the entanglement of formation of a bipartite state is generally difficult, but special symmetries of a state can simplify the problem. For instance, this allows one to determine the entanglement of formation of Werner states and…

We study experimentally what is arguably the simplest yet non-trivial colloidal system: two-dimensional clusters of 6 spherical particles bound by depletion interactions. These clusters have multiple, degenerate ground states whose…