Quantum information science may lead to technological breakthroughs in computing, cryptography, and sensing. For the implementation of these tasks, however, complex devices with many components are needed quantum advantage easily be spoiled by failure only a few parts. A paradigmatic example is networks. There, not do noise sources such as photon absorption or imperfect memories long waiting times low fidelity, but also hardware break, leading dysfunctionality entire network. successful...

Entanglement purification describes a primitive in quantum information processing, where several copies of noisy states are distilled into few nearly pure high quality via local operations and classical communication. Especially the multiparticle case, task entanglement is complicated, as many inequivalent forms state exist protocols need to be tailored for different target states. In this paper we present optimized hypergraph states, which form family multiqubit that relevant from...

The CHSH inequalities are the most famous examples of Bell inequalities. Cabello, Severini, and Winter (CSW) came up with a graph approach to noncontextuality inequalities, which connects some graph-theoretic concepts quantum classical correlations. For example, theta body exclusivity can be associated set correlations achieved by theory. Following CSW approach, one may think that graph, is equal inequality, but this really true? All assumptions about come from scenarios, while only demands...

Cluster states and graph in general offer a useful model of the stabilizer formalism path toward development measurement-based quantum computation. Their defining structure -- group encodes all possible correlations which can be observed during measurement. Those outcomes are compatible with make error correction possible. Here, we leverage both properties to design feasible families that used as robust building blocks This procedure reduces effect experimentally relevant noise models on...

Graph states are a class of multi-partite entangled quantum that ubiquitous in many networking applications; the study equivalence relations between graph under local operations aims to provide methods relate networked settings. The problem determining unitary (LU) is NP, and it remains an open question if efficient general possible. We introduce family easy-to-compute LU-invariants based on marginal structure graphs allow rule out states. show these invariants can uniquely identify all...

We provide a graphical method to describe and analyze non-Gaussian quantum states using hypergraph framework. These are pivotal resources for computing, communication, metrology, but their characterization is hindered by complex high-order correlations. The formalism encapsulates transformation rules any Gaussian unitary operation local quadrature measurement, offering visually intuitive tool manipulating such through experimentally feasible pathways. Notably, we develop methods the...

We present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces problem to solving a system linear equations in modular arithmetic. Furthermore, we demonstrate that any LU between two states takes specific form, naturally generalizing class Clifford (LC) equivalences. Lastly, using existing libraries, verify up $n=11$, number LC orbits is identical.

Entanglement purification describes a primitive in quantum information processing, where several copies of noisy states are distilled into few nearly-pure high quality via local operations and classical communication. Especially the multiparticle case, task entanglement is complicated, as many inequivalent forms pure state exist protocols need to be tailored for different target states. In this paper we present optimized hypergraph states, which form family multi-qubit that relevant from...

The CHSH inequalities are the most famous examples of Bell inequalities. Cabello, Severini, and Winter (CSW) came up with a graph approach to noncontextuality inequalities, which connects some graph-theoretic concepts quantum classical correlations. For example, theta body exclusivity can be associated set correlations achieved by theory. Following CSW approach, one may think that graph, is equal inequality, but this really true? All assumptions about come from scenarios, while only demands...

Quantum information science may lead to technological breakthroughs in computing, cryptography and sensing. For the implementation of these tasks, however, complex devices with many components are needed quantum advantage easily be spoiled by failure few parts only. A paradigmatic example networks. There, not only noise sources like photon absorption or imperfect memories long waiting times low fidelity, but also hardware break, leading a dysfunctionality entire network. successful long-term...