Related papers: Transformations of Stabilizer States in Quantum Ne…
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.…
This work is concerned with multi-party stabilizer states in the sense of quantum information theory. We investigate the homological invariants for states of which each party holds a large equal number N of quantum bits. We show that in…
The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
The stabilizer group of an n-qubit state \psi is the set of all matrices of the form g=g_1\otimes\cdots\otimes g_n, with g_1,...,g_n being any 2x2 invertible complex matrices, that satisfy g\psi=\psi. We show that for 5 or more qubits,…
Non-symmetric GHZ states ($n$-GHZ$_\alpha$), defined by unequal superpositions of $|00...0>$ and $|11...1>$, naturally emerge in experiments due to decoherence, control errors, and state preparation imperfections. Despite their relevance in…
We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…
Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
Graph states are ubiquitous in quantum information with diverse applications ranging from quantum network protocols to measurement based quantum computing. Here we consider the question whether one graph (source) state can be transformed…
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…
Characterizing large noisy multiparty quantum states using genuine multiparty entanglement is a challenging task. In this paper, we calculate lower bounds of genuine multiparty entanglement localized over a chosen multiparty subsystem of…
We consider the explicit construction of resource states for measurement-based quantum information processing. We concentrate on special-purpose resource states that are capable to perform a certain operation or task, where we consider…
While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…
In this article we investigate the possibility of encoding classical information onto multipartite quantum states in the distant laboratory framework. We show that for all states generated by Clifford operation there always exist such an…
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…
We propose a new kind of invariant of multi-party stabilizer states with respect to local Clifford equivalence. These homological invariants are discrete entities defined in terms of the entanglement a state enjoys with respect to arbitrary…
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a…
We develop a topological framework for preparing families of non-stabilizer states, and computing their entanglement entropies, in $SU(2)_1$ Chern-Simons theory. Using the Kac-Moody algebra, we construct Pauli and Clifford operators as path…
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…