I am a researcher in data science at the Semantic Technology Institute Innsbruck. Before that, I was a researcher in quantum information theory. I was—and still am—interested in multipartite entanglement and complex networks.
I studied physics at Universitat Autònoma de Barcelona, spending the last year in Pisa, where I did the Tesi di Laurea Specialistica. I have a MSc in Photonics from Universitat Politècnica de Catalunya.
I obtained my PhD at the Quantum Information Group in Universitat Autònoma de Barcelona, under the supervision of John Calsamiglia. The title of my thesis was “Entanglement distribution in quantum complex networks”.
I also had a postdoctoral position at the Quantum Information Theory group of Barbara Kraus in Innsbruck.
This thesis deals with the study of quantum networks with a complex structure, the implications this structure has in the distribution of entanglement and how their functioning can be enhanced by operating in the quantum regime.
David Sauerwein, Katharina Schwaiger, Martí Cuquet, Julio I. de Vicente, Barbara Kraus
Entanglement is the resource to overcome the natural limitations of spatially separated parties restricted to Local Operations assisted by Classical Communications (LOCC). Recently two new classes of operational entanglement measures, the source and the accessible entanglement, for arbitrary multipartite states have been introduced. Whereas the source entanglement measures from how many states the state of interest can be obtained via LOCC, the accessible entanglement measures how many states can be reached via LOCC from the state at hand. We consider here pure bipartite as well as multipartite states and derive explicit formulae for the source entanglement. Moreover, we obtain explicit formulae for a whole class of source entanglement measures that characterize the simplicity of generating a given bipartite pure state via LOCC. Furthermore, we show how the accessible entanglement can be computed numerically. For generic four-qubit states we first derive the necessary and sufficient conditions for the existence of LOCC transformations among these states and then derive explicit formulae for their accessible and source entanglement.
Katharina Schwaiger, David Sauerwein, Martí Cuquet, Julio I. de Vicente, Barbara Kraus
We introduce two operational entanglement measures which are applicable for arbitrary multipartite (pure or mixed) states. One of them characterizes the potentiality of a state to generate other states via local operations assisted by classical communication (LOCC) and the other the simplicity of generating the state at hand. We show how these measures can be generalized to two classes of entanglement measures. Moreover, we compute the new measures for few-partite systems and use them to characterize the entanglement contained in a three-qubit state. We identify the GHZ- and the W-state as the most powerful three-qubit states regarding state manipulation.
Otfried Gühne, Martí Cuquet, Frank E.S. Steinhoff, Tobias Moroder, Matteo Rossi, Dagmar Bruß, Barbara Kraus, Chiara Macchiavello
Journal of Physics A 47, 335303 (2014)
Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well-established notion of graph states. Mathematically, they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states; alternatively, they can also be phrased in terms of a non-local stabilizer formalism. In this paper, we explore the entanglement properties and nonclassical features of hypergraph states. First, we identify the equivalence classes under local unitary transformations for up to four qubits, as well as important classes of five- and six-qubit states, and determine various entanglement properties of these classes. Second, we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph-theoretical interpretation. Finally, we consider the question whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories. We demonstrate that various noncontextuality inequalities and Bell inequalities can be derived for hypergraph states.
Martí Cuquet and John Calsamiglia
Physical Review A 86, 042304 (2012)
We propose a scheme to distribute graph states over quantum networks in the presence of noise in the channels and in the operations. The protocol can be implemented efficiently for large graph sates of arbitrary (complex) topology. We benchmark our scheme with two protocols where each connected component is prepared in a node belonging to the component and subsequently distributed via quantum repeaters to the remaining connected nodes. We show that the fidelity of the generated graphs can be written as the partition function of a classical Ising-type Hamiltonian. We give exact expressions of the fidelity of the linear cluster and results for its decay rate in random graphs with arbitrary (uncorrelated) degree distributions.
Martí Cuquet and John Calsamiglia
Physical Review A 83, 032319 (2011)
We study entanglement distribution in quantum complex networks where nodes are connected by bipartite entangled states. These networks are characterized by a complex structure, which dramatically affects how information is transmitted through them. For pure quantum state links, quantum networks exhibit a remarkable feature absent in classical networks: it is possible to effectively rewire the network by performing local operations on the nodes. We propose a family of such quantum operations that decrease the entanglement percolation threshold of the network and increase the size of the giant connected component. We provide analytic results for complex networks with an arbitrary (uncorrelated) degree distribution. These results are in good agreement with numerical simulations, which also show enhancement in correlated and real-world networks. The proposed quantum preprocessing strategies are not robust in the presence of noise. However, even when the links consist of (noisy) mixed-state links, one can send quantum information through a connecting path with a fidelity that decreases with the path length. In this noisy scenario, complex networks offer a clear advantage over regular lattices, namely, the fact that two arbitrary nodes can be connected through a relatively small number of steps, known as the small-world effect. We calculate the probability that two arbitrary nodes in the network can successfully communicate with a fidelity above a given threshold. This amounts to working out the classical problem of percolation with a limited path length. We find that this probability can be significant even for paths limited to few connections and that the results for standard (unlimited) percolation are soon recovered if the path length exceeds by a finite amount the average path length, which in complex networks generally scales logarithmically with the size of the network.
Martí Cuquet and John Calsamiglia
Physical Review Letters 103, 240503 (2009)
Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here, we study the effect of entanglement percolation as a means to establish long-distance entanglement between arbitrary nodes of quantum complex networks. We develop a theory to analytically study random graphs with arbitrary degree distribution and give exact results for some models. Our findings are in good agreement with numerical simulations and show that the proposed quantum strategies enhance the percolation threshold substantially. Simulations also show a clear enhancement in small-world and other real-world networks.