Related papers: Limitations of Quantum Coset States for Graph Isom…
We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by…
How can we use a quantum computer to detect the entanglement structure of a quantum state? Bouland et al. (2024) recently provided an algorithm that, given multiple input copies of the state, finds the "hidden cuts"-partitions into fully…
Quantum states featuring extensive multipartite entanglement are a resource for quantum-enhanced metrology, with sensitivity up to the Heisenberg limit. However, robust generation of these states using unitary dynamics typically requires…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
The graph state formalism is a useful abstraction of entanglement. It is used in some multipartite purification schemes and it adequately represents universal resources for measurement-only quantum computation. We focus in this paper on the…
We consider quantum graph states that can be mapped to directed weighted graphs, also known as directed networks. The geometric measure of entanglement of the states is calculated for the quantum graph states corresponding to arbitrary…
We investigate which entanglement resources allow universal measurement-based quantum computation via single-qubit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other…
We study a generalization of entanglement testing which we call the "hidden cut problem." Taking as input copies of an $n$-qubit pure state which is product across an unknown bipartition, the goal is to learn precisely where the state is…
An experimental scheme is proposed for building massively multipartite entangled states using both the spatial and the frequency modes of an optical parametric oscillator. We provide analytical forms of the entangled states using the…
The measurement based, or one-way, model of quantum computation for continuous variables uses a highly entangled state called a cluster state to accomplish the task of computing. Cluster states that are universal for computation are a…
We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more…
We consider graph states generated by the action of controlled phase shift operators on a separable state of a multi-qubit system. The case when all the qubits are initially prepared in arbitrary states is investigated. We obtain the…
We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian projected entangled pair states (GPEPS), we show that no matter what Gaussian local measurements are…
Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems…
Many exponential speedups that have been achieved in quantum computing are obtained via hidden subgroup problems (HSPs). We show that the HSP over Weyl-Heisenberg groups can be solved efficiently on a quantum computer. These groups are…
Graph Isomorphism is such an important problem in computer science, that it has been widely studied over the last decades. It is well known that it belongs to NP class, but is not NP-complete. It is thought to be of comparable difficulty to…
Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement…
In the realm of quantum information processing, the efficient characterization of entangled states poses an overwhelming challenge, rendering the traditional methods including quantum tomography unfeasible and impractical. To tackle this…
Weighted graph states are a natural generalization of graph states, which are generated by applying controlled-phase gates, instead of controlled-Z gates, to a separable state. In this paper, we show that uniformly weighted graph states on…
We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory,…