arXiv subjects

Lina Vandré

Publications and source records attributed to Lina Vandré.

8 recordsLinked to original sources

arXiv2026

Useful entanglement can be extracted from noisy graph states

Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure - the stabilizer group - encodes all possible correlations that can be observed during measurement. The measurement outcomes which are consistent with the stabilizer structure make error correction possible. Here, we leverage both properties to design feasible families of states that can be used as robust building blocks of quantum computation. This procedure reduces the effect of experimentally relevant noise models on the extraction of smaller entangled states from the larger noisy graph state. In particular, we study the extraction of Bell pairs from linearly extended graph states - this has the immediate consequence for state teleportation across the graph. We show that robust entanglement can be extracted by proper design of the linear graph with only a minimal overhead of the physical qubits. This scenario is relevant to systems in which the entanglement can be created between neighboring sites. The results shown in this work provide a mathematical framework for noise reduction in measurement-based quantum computation. With proper connectivity structures, the effect of noise can be minimized for a large class of realistic noise processes.

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arXiv2025

Graph state extraction from two-dimensional cluster states

We propose schemes to extract arbitrary graph states from two-dimensional cluster states by locally manipulating the qubits solely via single-qubit measurements. We introduce graph state manipulation tools that allow one to increase the local vertex degree and to merge subgraphs. We utilize these tools together with the previously introduced zipper scheme that generates multiple edges between distant vertices to extract the desired graph state from a two-dimensional cluster state. We show how to minimize overheads by avoiding multiple edges, and compare with a local manipulation strategy based on measurement-based quantum computation together with transport. These schemes have direct applications in entanglement-based quantum networks, sensor networks, and distributed quantum computing in general.

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arXiv2025

Graphical Framework for Non-Gaussian Quantum States

We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered by their complex high-order correlations. The framework encapsulates transformation rules for a series of typical Gaussian unitary operation and local quadrature measurement, offering a visually intuitive tool for manipulating such states through experimentally feasible pathways. Notably, we develop methods for the generation of complex hypergraph states with more or higher-order hyperedges from simple structures through Gaussian operations only, facilitated by our graphical rules. We present illustrative examples on the preparation of non-Gaussian states rooted in these graph-based formalisms, revealing their potential to advance continuous-variable general quantum computing capabilities.

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arXiv2025

Distinguishing Graph States by the Properties of Their Marginals

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 in networked settings. Based on the marginal structure of graph states, we introduce a family of easy-to-compute LU-invariants. We show that these invariants uniquely identify the entanglement classes of every graph state up to 8 qubits and discuss their reliability for larger numbers of qubits. To handle larger graphs, we generalize tools to test for local Clifford (LC) equivalence of graph states that work by condensing large graphs into smaller graphs. In turn, we show that statements on the equivalence of these smaller graphs (which are easier to compute) can be used to infer statements on the equivalence of the original, larger graphs. We analyze LU-equivalence in two key settings - with and without allowing for the permutation of qubits. We identify entanglement classes, whose marginal structure does not allow us to distinguish them. As a result, we increase the bound on the number of qubits where the LU-LC conjecture holds from 8 to 10 qubits in the setting where qubit permutations are allowed.

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arXiv2025

Algorithm to Verify Local Equivalence of Stabilizer States

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 transformation between two graph states takes a specific form, naturally generalizing the class of local Clifford (LC) transformations. Lastly, using existing libraries, we verify that for up to $n=11$, the number of LU and LC orbits of stabilizer states is identical.

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arXiv2024

Aging and Reliability of Quantum Networks

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 and the quantum advantage may easily be spoiled by failure of few parts only. A paradigmatic example are quantum networks. There, not only noise sources like photon absorption or imperfect quantum memories lead to long waiting times and low fidelity, but also hardware components may break, leading to a dysfunctionality of the entire network. For the successful long-term deployment of quantum networks in the future, it is important to take such deterioration effects into consideration during the design phase. Using methods from reliability theory and the theory of aging we develop an analytical approach for characterizing the functionality of networks under aging and repair mechanisms, also for non-trivial topologies. Combined with numerical simulations, our results allow to optimize long-distance entanglement distribution under aging effects.

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arXiv2024

Entanglement Purification of Hypergraph States

Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into few copies of nearly-pure states of high quality via local operations and classical communication. Especially in the multiparticle case, the task of entanglement purification is complicated, as many inequivalent forms of pure state entanglement exist and purification protocols need to be tailored for different target states. In this paper we present optimized protocols for the purification of hypergraph states, which form a family of multi-qubit states that are relevant from several perspectives. We start by reformulating an existing purification protocol in a graphical language. This allows for systematical optimization and we present improvements in three directions. First, one can optimize the sequences of the protocol with respect to the ordering of the parties. Second, one can use adaptive schemes, where the measurement results obtained within the protocol are used to modify the protocols. Finally, one can improve the protocol with respect to the efficiency, requiring fewer copies of noisy states to reach a certain target state.

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arXiv2023

Quantum sets of the multicolored-graph approach to contextuality

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 to quantum and classical correlations. For example, the theta body of the exclusivity graph can be associated with the set of correlations achieved by quantum theory. Following the CSW approach, one may think that the theta body of the CHSH graph, is equal to the quantum set of the CHSH Bell inequality, but is this really true? All assumptions about the CHSH inequalities come from Bell scenarios, while CSW approach only demands the exclusivity structure of a non-contextuality (NC) scenario. To deal with the extra structure related to the presence of different players in a Bell scenario like CHSH, the colored-graph approach was introduced. Does it make any difference to think about CHSH as a Bell scenario or a more general NC scenario? The Bell CHSH inequality is represented by a bicolored graph and the NC CHSH inequality by a simple graph, which is the shadow of the colored graph. In general, we have that the theta body of the colored graph is a subset of the theta body of its shadow graph in the same way that the Lovàsz number, which corresponds to the quantum bound, of the simple graph is greater than or equal to the Lovàsz number of the colored graph. In the case of the CHSH inequality, we have that the Lovàsz numbers are equal. Does this accident also hold for the corresponding quantum sets? Is it true that the theta bodies are equal, which would mean that every correlation reached by quantum theory applied to the CHSH NC scenario could also be obtained at the in principle more restrictive CHSH Bell scenario? In this paper our answer to such a question is negativ. This implies that there are quantum correlations which can not be obtained under Bell restrictions.

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