相关论文: Graphical description of the action of Clifford op…

We translate the action of local Clifford operations on graph states into transformations on their associated graphs - i.e. we provide transformation rules, stated in purely graph theoretical terms, which completely characterize the…

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…

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…

The form of a local Clifford (LC, also called local Gaussian (LG)) operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit…

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.…

We use a graphical representation of stabilizer states to describe, simply and efficiently, the effect of measurements of Pauli products on stabilizer states. This work complements our earlier work [Phys. Rev. A 77, 042307 (2008)], which…

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…

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)…

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…

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…

We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…

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…

Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…

We describe the structure of the $n$-qubit Clifford group $C_n$ via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we…

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…

In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as \emph{local complementation}. It was shown that two…

We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the…

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…

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…

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…