相关论文: Compact set of invariants characterizing graph sta…

Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for…

Graph states are a class of multi-partite entangled quantum states that are ubiquitous in quantum information. We study equivalence relations between graph states under local unitaries (LU) to obtain distinguishing methods both in local and…

Three new graph invariants are introduced which may be measured from a quantum graph state and form examples of a framework under which other graph invariants can be constructed. Each invariant is based on distinguishing a different number…

The entanglement of graph states up to eight qubits is calculated in the regime of iteration calculation. The entanglement measures could be the relative entropy of entanglement, the logarithmic robustness or the geometric measure. All 146…

Graph states represent a significant class of multi-partite entangled quantum states with applications in quantum error correction, quantum communication, and quantum computation. In this work, we introduce a novel formalism called the…

We show how to prepare any graph state of up to 12 qubits with: (a) the minimum number of controlled-Z gates, and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any…

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the…

Several entanglement measures are used to define equivalence classes in the set of hypergraph states of three qubits. Our classifications reveal that (i) under local unitary transformations, hypergraph states of three qubits are split into…

Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a…

We investigate the properties of different levels of entanglement in graph states which correspond to connected graphs. Combining the operational definition of graph states and the postulates of entanglement measures, we prove that in…

We propose a new classification for the entanglement in graph states based on generalized con- currence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in…

Graph states and their entanglement properties are pivotal for the development of quantum computing and technologies. For qubits, local complementation, a graphical rule that connects all the equivalent states under Local Clifford (LC)…

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…

Verstraete, Dehaene, and De Moor (2003) showed that SLOCC invariants provide entanglement monotones. We observe that many highly entangled or useful four-qubit states that appear in prior literature are stationary points of such…

We compare the polynomial invariants for four qubits introduced by Luque and Thibon, PRA {\bf 67}, 042303 (2003), with optimized Bell inequalities and a combination of two qubit concurrences. It is shown for various parameter dependent…

It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the…

The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…

This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the…

We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local…

We propose a new approach to the geometry of the four-qubit entanglement classes depending on parameters. More precisely, we use invariant theory and algebraic geometry to describe various stratifications of the Hilbert space by SLOCC…