Related papers: Local Unitary Representation of Braids and N-Qubit…
We study the entanglement structure of tripartite stabilizer states on $N$ qudits of dimension $D$, distributed across parties $A$, $B$, and $C$, under arbitrary local unitaries. Prior work by Bravyi et al. and Looi et al. showed that qubit…
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary $R$-matrix and to a simple object in a unitary braided fusion category. Unitary $R$-matrices, namely unitary solutions to 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…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a…
We refine recent local unitary entanglement classification for symmetric pure states of $n$ qubits (that is, states invariant under permutations of qubits) using local unitary stabilizer subgroups and Majorana configurations. Stabilizer…
We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parameterized by diagrams of nonintersecting chords…
Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their…
The relationships between quantum entangled states and braid matrices have been well studied in recent years. However, most of the results are based on qubits. In this paper, We investigate the applications of 2-qutrit entanglement in the…
The entanglement properties of a multiparty pure state are invariant under local unitary transformations. The stabilizer dimension of a multiparty pure state characterizes how many types of such local unitary transformations existing for…
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…
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 investigate the relation between local unitary symmetries and entanglement invariants of multi-qubit systems. The Hilbert space of such systems can be stratified in terms of states with different types of symmetry. We review the…
The robustness properties of bipartite entanglement in systems of N bosons distributed in M different modes are analyzed using a definition of separability based on commuting algebras of observables, a natural choice when dealing with…
Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states…
Local unitary stabilizer subgroups constitute powerful invariants for distinguishing various types of multipartite entanglement. In this paper, we show how stabilizers can be used as a basis for entanglement verification protocols on…
This paper gives a criterion for detecting the entanglement of a quantum state, and uses it to study the relationship between topological and quantum entanglement. It is fundamental to view topological entanglements such as braids as…
Braid theories are applied to quantum computation processes, where to each crossing in the Braid diagram a unitary Yang-Baxter operator R is associated, representing either a Braiding matrix or a universal quantum gate. By operating with…
We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…
We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.