Related papers: Geometric picture for SLOCC classification of pure…

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…

Entanglement properties of a basic set of eight entangled three particle pure states possessing certain permutation symmetries are studied. They fall into four sets of two entangled states, differing in their patterns of robustness to…

We introduce an operational entanglement classification of symmetric mixed states for an arbitrary number of qubits based on stochastic local operations assisted with classical communication (SLOCC operations). We define families of SLOCC…

The Bloch sphere is a familiar and useful geometrical picture of the dynamics of a single spin or two-level system's quantum evolution. The analogous geometrical picture for three-level systems is presented, with several applications. The…

The full Schmidt decomposition of spatiotemporally entangled states generated from spontaneous parametric down-conversion (SPDC) has not been carried out until now due to the immense computational complexity arising from the large…

The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…

We give a fermionic Fock space description of embedded entangled qubits. Within this framework the problem of classification of pure state entanglement boils down to the problem of classifying spinors. The usual notion of separable states…

While multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols, obtaining a high-level, structural understanding of entanglement involving arbitrarily many qubits is a long-standing open…

We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of…

We examine the geometric structure of qutrit state space by identifying the outcome probabilities of symmetric informationally complete (SIC) measurements with quantum states. We categorize the infinitely many qutrit SICs into eight SIC…

The unitary group acting on the Hilbert space of three quantum bits admits a Lie subgroup, of elements which permute with the symmetric group of permutations. Under the action of such Lie subgroup, the Hilbert space splits into three…

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…

Detection and classification of entanglement properties of a multi-qubit system is a topic of great interest. This topic has been studied extensively and thus we found different approaches for the detection and classification of multi-qubit…

The set of quantum states consists of density matrices of order $N$, which are hermitian, positive and normalized by the trace condition. We analyze the structure of this set in the framework of the Euclidean geometry naturally arising in…

In [M. Walter et al., Science 340, 1205, 7 June (2013)], via polytopes they gave a sufficient condition for genuinely entangled pure states and discussed SLOCC classification. In this paper, we study entanglement classification of pure…

We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks…

We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewritten the conifold or the Segre variety we can get…

We use the concept of \textit{entangled graphs} with weighted edges to present a classification for four-qubit entanglement which is based neither on the LOCC nor the SLOCC. Entangled graphs, first introduced by Plesch et al. [Phys. Rev. A…

We provide new examples of pure entangled systems related to cluster state quantum computation that can be efficiently simulated classically. In cluster state quantum computation input qubits are initialised in the `equator' of the Bloch…

Let E' denote the set of non-normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). We show that the set of SLOCC equivalence classes of states in E', equipped with the quotient topology, is…