Related papers: The Structure of Circle Graph States
Graph states form a large family of quantum states that are in one-to-one correspondence with mathematical graphs. Graph states are used in many applications, such as measurement-based quantum computation, as multipartite entangled…
Stabilizer states form a ubiquitous family of quantum states that can be graphically represented through the graph state formalism. A fundamental property of graph states is that applying a local complementation - a well-known and…
Classifying locally equivalent graph states, and stabilizer states more broadly, is a significant problem in the theories of quantum information and multipartite entanglement. A special focus is given to those graph states for which…
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…
The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical…
We present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic. Furthermore, we demonstrate that any LU…
Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus…
Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to…
Graph states are a fundamental class of multipartite entangled quantum states with wide-ranging applications in quantum information and computation. In this work, we develop a systematic framework for constructing and analyzing…
Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are…
Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states.…
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…
It was once conjectured that two graph states are local unitary (LU) equivalent if and only if they are local Clifford (LC) equivalent. This so-called LU-LC conjecture was disproved in 2007, as a pair of 27-qubit graph states that are…
Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same. Despite the fact this settles the LU-LC conjecture, a sufficient…
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.…
Graph states are computationally powerful quantum states with many applications including use as resource states for measurement-based quantum computing (MBQC). We demonstrate construction of graph states on a Rydberg atom quantum analogue…
The name graph state is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
Graph states are the main computational building blocks of measurement-based computation and a useful tool for error correction in the gate model architecture. The graph states form a class of quantum states which are eigenvectors for the…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…