Related papers: Local Equivalences of Graph States
There are local operators on (labeled) graphs $G$ with labels $(g_{ij})$ coming from a finite field. If the filed is binary, in other words, if the graph is ordinary, the operation is just the local complementation. That is, to choose a…
Local sets, a graph structure invariant under local complementation, have been originally introduced in the context of quantum computing for the study of quantum entanglement within the so-called graph state formalism. A local set in a…
Graph states are a powerful class of entangled states with numerous applications in quantum communication and quantum computation. Local Clifford (LC) operations that map one graph state to another can alter the structure of the…
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC)…
Local complementation of a graph $G$ on vertex $v$ is an operation that results in a new graph $G*v$, where the neighborhood of $v$ is complemented. Two graph are locally equivalent if on can be reached from the other one through local…
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of…
We report progress on the LU-LC conjecture - an open problem in the context of entanglement in stabilizer states (or graph states). This conjecture states that every two stabilizer states which are related by a local unitary operation, must…
Orbits of graphs under local complementation (LC) and edge local complementation (ELC) have been studied in several different contexts. For instance, there are connections between orbits of graphs and error-correcting codes. We define a new…
Graph states are a key resource for measurement-based quantum computation and quantum networking, but state-preparation costs limit their practical use. Graph states related by local complement (LC) operations are equivalent up to…
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…
A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism.…
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a…
Hypergraph states form a family of multiparticle quantum states that generalizes cluster states and graph states. We study the action and graphical representation of nonlocal unitary transformations between hypergraph states. This leads to…
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…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
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…
The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists…
The necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations derived in [B. Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…