## Workshop de Información Cuántica

en España

Madrid, Septiembre 17-19, 2012

Horario | Lunes 17 | Martes 18 | Miércoles 19 |

9:30 | A. Cabello | R. Orús | A. Acín |

G. Sentís Herrera F. Galve | O. Viyuela J. Molina | M. Tíerz | |

11:30 | Café | ||

12:00 | D. Pérez-García | E. Rico | D. Porras |

A. Belén Sáinz | J. de Vicente | D. Zueco | |

14:00 | Comida | ||

16:00 | M. Lewenstein | E. Solano | M. Mitchell |

R. Zambrini A. Rivas | L. Lamata J. Casanova | M. Cristiani J. Siewert | |

Café + pósters | Café | Café | |

18:00 | J. Calsamiglia | G. Toth | |

V. Fernández J. García López | Reunión GEIC | ||

21:00 | Cena |

Charlas invitadas: 45 minutos (40 presentación + 5 preguntas). Charlas contribuídas: 25 minutos (20 + 5)

## Charlas invitadas

**Graph approach to quantum correlations**

Adán Cabello (Univ. Sevilla)

Every non-contextuality (NC) inequality (including ever Bell inequality) can be mapped into a graph so that three characteristic numbers of this graph provide the maximum non-contextual, quantum, and general probabilistic bounds. Reciprocally, every graph can be mapped into a NC inequality for which quantum correlations attaining the maximum violation exist. This shows that graphs are a powerful tool to obtain quantum contextual correlations on demand. We apply this to identify all graphs with less than 11 vertices which correspond to correlations with (i) quantum vs non-contextual advantage, (ii) quantum-but-no-post-quantum advantage, and (iii) no-quantum-but-post-quantum advantage. Some interesting inequalities obtained with this method and some recent experiments based on these ideas are presented.

**Robustness of 2d topological order and cluster states using infinite Projected Entangled Pair States methods**

Román Orús (MPQ Garching, Alemania)

We investigate the stability of the topological phases of the Z2 and Z3 Toric Code models and the 2d Cluster State Hamiltonian in the presence of uniform magnetic fields by means of infinite Projected Entangled Pair State algorithms (iPEPS) and series expansion techniques. We find that when the perturbation is strong enough, the systems undergo a plethora of phase transitions whose first- or second-order nature depends on the field orientation and symmetry. The phase diagrams of these systems are investigated.

**Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench**

E. Rico (IQOQI, Innsbruck)

Using a fermi-bose mixture of ultra-cold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermonic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerges from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.

D. Banerjee, M. Dalmonte, M. Müller, E. Rico, P. Stebler, U.-J. Wiese, P. Zoller, arXiv:1205.6366

## Charlas contribuídas

**Corrección de errores de Shor con una sóla molécula**

Alejandro Gaita Ariño (ICMOL, Univ. Valencia)

Los códigos de corrección cuántica de errores son cruciales para el procesamiento cuántico de información. El código de Shor usa nueve qubits para codificar y proteger a un qubit de errores arbitrarios que afecten a un único qubit. Se mostrará que la estructura compleja del estado fundamental de una molécula que contiene tres iones 159Tb3+ es equivalente a nueve qubits electro-nucleares. Se presenta el esquema general para implementar el código de Shor en tales moléculas en un experimento de tipo Electron-Nuclear DOuble Resonance (ENDOR). Se ofrecerán indicaciones concretas para dos sub-códigos relevantes y se discutirán dos sistemas moleculares que podrían ser adecuados desde un punto de vista experimental: [{Tb(TETA)}2 Tb(H2O)8 ]+ y Tb3 Q9 (TETA=ácido 1,4,8,11-tetraazaciclotetradecano-1,4,8,11-tetraacético, Q=quinolinato).

**Theory of time- and frequency-resolved N-photon correlations**

A. Gonzalez-Tudela (Univ. Autónoma de Madrid)

Experimentally, the study of correlations between peaks of photoluminescence spectra is common practice in cavity-QED systems [1]. This provides valuable information about the dynamics of the bare and dressed states (polaritons), especially in out-of-equilibrium systems [2], where polaritons may not be well defined and the spectra may become too complex. However an adequate theoretical description of this powerful experimental procedure is stilllacking. Frequency resolved correlation functions are, indeed, difficult to obtain theoretically

and have received very little attention up to now [3]. We develop a general theory of frequency and time resolved correlation functions [4] valid for steady state situations under continuous excitation or for the decay dynamics after pulsed excitation with a linear scale of the complexity of computation rather than exponential. The linewidths of the detectors need to be explicitely taken into account and become relevant variables to describe the system. We apply our theory to different fundamental cases such as resonance fluorescence (Mollow triplet) and the different peaks of the Jaynes- Cummings model, i. e. Rabi doublet. showing how correlations of various peaks at zero or finite time delays bring new insights into the dynamics of open quantum systems providing predictions and guidance for the experiments.

[1] K. Hennessy et al., Nature 445, 896 (2007), A. Ulhaq, et al, Nat. Photon. (2012).

[2] FP. Laussy et al., PRL 101, 083601 (2008); E. del Valle & FP. Laussy. PRL 105, 233601 (2010).

[3] Joosten & Nienhuis, J. Opt. B 2, 158 (2000); Bel & Brown, PRL 102, 018303 (2009).

[4] E. del Valle, A. Gonzalez-Tudela et al.,(2012) arXiv:1203.6016v1

**Local Orthogonality: a multipartite principle for (quantum) correlations**

Ana Belén Sainz (ICFO)

Foundations of Quantum Mechanics is nowadays a subject of intense debate, searching for "physical" rather than "mathematical" axioms for quantum theory. Characterizing the set of quantum correlations might be an important aspect of this and is an interesting problem on its own. Several candidate axioms for quantum correlations have been proposed, such as "Information Causality" and "non-trivial Communication Complexity". Even though they successfully applied to some concrete scenarios, they have a fundamental limitation: to be based on bipartite information concepts, which proved to be insufficient when moving to the multipartite scenario. In this work, we present a naturally multipartite principle which could shed light on the understanding of this topic.

We present the "Local Orthogonality" principle as: "the sum of the probability of orthogonal events' occurrence is less or equal than one". In the terminology used for correlations, we consider two "events" to be orthogonal if there exists a party that in both happens to measure the same input but obtains different outputs. We established a connection between LO and Graph Theory, which in scenarios with larger number of parties, inputs or outputs, happens to be of much convenience. By means of this we see that, even though we prove LO is equivalent to the non-signaling principle for the bipartite case, in a scenario with more than 2 parties a rich structure appears. Combining this in networkings, we show that LO discards supra-quantum boxes which can not be identified by bipartite information principles, and furthermore we are able to get close to the quantum set.

*Formalizing the existence of entanglement under fractional **magnetization or long-range interactions*

Andrea Cadarso Rebolledo (UCM / IFF, CSIC)

Entanglement plays a central role in many-body quantum systems as it can be used to understand the structure of the quantum states that appear in nature. In systems governed by short-range interactions, low energy states possess very little entanglement. In contrast, states evolved after quenches display large amounts of entanglement. Apart from the cases mentioned above, there exist practically no other physical situation where the existence of large or small amounts of entanglement can be rigorously established. In this talk, we identify two other scenarios in one spatial dimension that can be connected to the presence of entanglement: namely the presence of fractionalization in the magnetization of the chain or the existence of long-range interactions.

**A Gottesman-Knill theorem for all finite Abelian groups**

Juan Bermejo Vega (MPQ, Garching)

Joint work with Maarten Van den Nest* The Gottesman-Knill theorem shows how a Heisenberg picture of quantum mechanics can be used to efficiently simulate classically a non-trivial class of quantum computations i.e. Clifford gates and Pauli measurements. In this work we consider a broader class of classical simulations whose main quantum ingredients are normaliser circuits and generalised Pauli-operator measurements. The latter class includes intriguing operations used in the design of quantum algorithms, namely, quantum Fourier transforms over Abelian groups---sometimes said to be the source of various exponential quantum speedups---. In spite of their apparent “quantumness”, we prove that efficient classical simulations of these circuits can be achieved. Our main result is a generalisation of the Gotteman-Knill theorem from n-qubit systems to finite Abelian groups, here used to model physical systems that may not be decomposable into products of small subsystems. The main techniques introduced are analytical and algorithmic methods to study and manipulate stabiliser codes on high dimensional systems, based on elements from group theory. The main reference for this work is an upcoming manuscript [1]. For a previous closely related work consult [2], by one of the authors. *Max Planck Institute of Quantum Optics, Garching, Germany. [1]: A Gottesman-Knill theorem for all finite Abelian groups. Juan Bermejo Vega, Maarten Van den Nest. [2]: Efficient classical simulations of quantum Fourier transforms and normalizer circuits over Abelian groups. Maarten Van den Nest.

**Bosonic Models within quantum circuits**

David Zueco Láinez (ICMA / Univ. Zaragoza)

We will present superconducting resonator architectures for coupled bosonic models in one and two dimensions. Our proposal allows real-time tunability of the coupling. The coupling can be engineered in form, being linear and non-linear or introducing a phase in the hopping (gauge fields), etc ... We will discuss several applications in all optical quantum computing, continuum variable quantum information and quantum simulation of e.g. polariton physics such as mott-superfluid phase or integer quantum Hall physics. Finally we introduce such architectures made out of superconducting circuits for dissipation driven quantum information tasks. We wil explain how-to engineer dissipation to achieve exotic phases in one dimensional coupled qubit-resonator arrays.

**Synthetic gauge fields for trapped ions**

Diego Porras Torre (Univ. Complutense de Madrid)

In this talk I will review some recent theoretical proposal for the quantum simulation of models from orbital quantum magnetism with trapped ions. First, I will introduce the concept of synthetic gauge fields induced by periodic drivings. This method can be applied to a variety of experimental setups to induce effective gauge fields. In the case of trapped ions, one can show that periodic drivings can induce effective transverse magnetic fields on the vibrational modes of ions trapped in a two-dimensional array of microtraps. This proposal may lead to the implementation of analogs of quantum Hall systems with phonons.

**Quantum discord of two qubits: maximally correlated states and sufficiency of perfect measurements**

Fernando Galve Conde (IFISC, CSIC)

We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states [1]. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. By random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of appearance of quantum and classical correlations for different ranks. We further show [2] that if general measurements (POVM) are taken instead of perfect (orthogonal) ones, a lower quantum discord can be found for rank 3, 4 two-qubit states, while for rank 2 states orthogonal measurements give the exact discord. The improvement given byPOVMs though, is almost negligible and occurs with very low probability in such Hilbert space. [1] F. Galve, G. L. Giorgi and R. Zambrini, Phys. Rev. A 83, 012102 (2011) [2] F. Galve, G. L. Giorgi and R. Zambrini, EPL 96, 40005 (2011)

**MOLECULAR NANOMAGNETS AS PROTOTYPES FOR SPIN-BASED QUANTUM LOGIC GATES**

Fernando Luis Vitalla (ICMA / Univ. Zaragoza)

In recent years, magnetic molecular clusters have been proposed as suitable materials for the realization of the quantum computer hardware. In this work, we argue that molecular clusters containing two lanthanide (e.g. Tb) magnetic ions meet all ingredients required to implement a universal CNOT quantum logic gate. The definition of control and target qubits is based on the strong magnetic anisotropy and the magnetic inequivalence of the two ions, which has been achieved by chemically engineering dissimilar coordination spheres. The magnetic asymmetry also provides a method to realize a SWAP gate in the same cluster. Electronic paramagnetic resonance experiments confirm that CNOT and SWAP transitions are not forbidden and provide a method to determine the decohernce time scales. Although we have mainly considered Tb2, for which the magnetic asymmetry can be easily determined on account of its large angular momentum, the same molecular structure can be realized with other lanthanide ions. This flexibility enables a vast choice of quantum gate designs, which will be also discussed. Molecular clusters are also stable in solution, which opens the additional possibility of depositing them onto quantum circuits, SQUIDs or rf superconducting resonators, able to manipulate its quantum spin state. Chemically engineered molecular quantum gates can therefore open promising avenues for the realization of scalable quantum computing architectures.

**Quantum learning without quantum memory**

Gael Sentís Herrera (Univ. Autónoma de Barcelona)

A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the very same error rate as the optimal (programmable) discrimination machine for any size of the training set. At variance with the latter, this machine can be used an arbitrary number of times without retraining. Its required (classical) memory grows only logarithmically with the number of training qubits, while (asymptotically) its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an ''estimate-and-discriminate" machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates. The machine is shown to be robust under possible imperfections in the initial setting.

**Spin squeezing inequalities for arbitrary spin**

Geza Toth (Ikerbasque / UPV-EHU)

We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in an ensemble in which the particles cannot be individually addressed. We also present a large set of criteria involving collective observables different from the angular momentum coordinates. We show that some of the inequalities can be used to detect k-particle entanglement and bound entanglement. Our work is important in experiments, since in most of the time the particles have a spin larger than 1/2 and the two-dimensional subsystem is created artificially. One reason for that is that most of the entanglement conditions are for particles with a spin j=1/2. With our inequalities it is now possible to detect entanglement in an ensemble of particles having a spin larger than 1/2.

**Free randomness distilation from arbitrarily little trusted sources.**

Gonzalo de la Torre Carazo (ICFO)

How sure can we be that there exists any truly random event in nature? Quantum theory predicts random outcomes when certain measurements are performed, but in principle there could be a higher theory governing each event that, should we knew about it, could help us better predict the outcomes of a measurement. John Bell showed that no local realistic theory can explain the measurements performed in a singlet, since they can violate a Bell Inequality which such local models must respect. Recently, Colbeck and Renner where able to improve Bell's result excluding any theory giving any better predictions than quantum theory, under the assumption that experimentalists can choose freely among different measurements at given times. This is the so called "free choice" assumption of Bell tests. In our present work, we relax this assumption allowing the experimental choices to be arbitrarily little trusted, letting them be almost maximally correlated with any other variable outside its future lightcone. We conclude then that the initial question has only two answers: either nature allows perfectly free and random events, or we live in a completely deterministic world.

**WKB analysis of relativistic Stern-Gerlach measurements**

Hans Westman (IFF-CSIC)

Spin is an important quantum degree of freedom in quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern-Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern-Gerlach operator is first motivated using the transformation properties of the electromagnetic field. Then, to confirm that this is indeed the correct operator, we provide a detailed analysis of the Stern-Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describing an interaction between a massive fermion and an electromagnetic field. Making use of the superposition principle we show that the +1 and −1 spin eigenstates of the proposed spin operator are split into separate packets due to the inhomogeneity of the Stern-Gerlach magnetic field. The operator we obtain is dependent on the momentum between particle and Stern-Gerlach apparatus, and is mathematically distinct from two other commonly used operators. The consequences for quantum tomography are considered.

**Quantum Networks and Environments: Principles and Simulation in Biology**

Javier Prior (Univ. Politécnica de Cartagena)

Multi-component quantum systems in strong interaction with their environment are getting increasing attention due to their importance in the accurate description of charge and energy transfer in bio-molecular aggregates. Unfortunately, these systems are very difficult to simulate as the system-bath interactions cannot be treated perturbatively and standard approaches are not valid or inefficient. We combine the Time-Evolving Block Decimation (TEBD) methods with techniques from the theory of orthogonal polynomials (OP) to provide an efficient method for simulating open quantum systems, including spin-boson models and their generalizations to multi-component systems. This method has been apply successfully to study pigment-protein complexes (PPCs) where its environmental spectral functions is knows to have significant frequency structure, including strong contributions from vibrational modes with frequencies comparable to the energy differences between excitonic excited states in PPCs. In this talk, the novel non-equilibirum dynamics induced in these resonant modes by the excitation of excitons will be shown to exert a non-trivial back action on the exciton dynamics which acts to generate or regenerate electronic coherences.

**Three-tangle for arbitrary three-qubit states**

Jens Siewert (UPV-EHU)

Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between

three or more quantum systems. Theory still does not provide adequate tools for this purpose. We put forward an analytical approach to determine the three-tangle for

arbitrary three-qubit mixed states. It is exact at least for a 20-parameter subfamily of states and gives nontrivial lower bounds for all other

states. That is why we call it a quantitative witness. Our method is based on the recently described Greenberger-Horne-Zeilinger (GHZ) symmetry and exact solutions for entanglement measures.

For arbitrary mixed two-qubit states the approach is equivalent to Wootters' method to compute the concurrence. Notably, our approach has the potential to be generalized both to higher qubit number and to higher-dimensional systems.

**Computación Cuántica Discreta**

Jesús García-López (Univ. Politécnica de Madrid)

La computación cuántica es una extensión de la computación clásica. Por tanto, el modelo cuántico de computación incluye, como un caso particular, al modelo clásico. La propiedad más importante del modelo clásico, en comparación con el modelo cuántico, consiste en que es fácil el control de errores. Por otro lado, la característica más importante del modelo cuántico, en comparación con el modelo clásico, es el paralelismo, que hace que el modelo cuántico sea, en principio, mucho más potente. Sin embargo, el modelo cuántico es un modelo continuo (analógico) para el que es difícil el control de errores, pese a la utilización de códigos cuánticos correctores de errores y de computación tolerante a fallos. Para quedarnos con lo mejor de cada uno de los modelos, introducimos un modelo intermedio, el modelo cuántico discreto, que mantiene el paralelismo cuántico, para poder mejorar la complejidad de determinados algoritmos clásicos, y que es discreto, para permitir un control de errores más eficiente. Algunos autores han propuesto otros tipos de discretización, pero con un enfoque distinto. Su objetivo es fundamentar teóricamente modelos discretos de la mecánica cuántica que permiten un cálculo eficiente de la evolución de estos sistemas. Nuestro modelo tiene un objetivo más concreto: obtener modelos de computación viables en los que exista paralelismo cuántico. El primer paso para construir un modelo discreto de computación cuántica consiste en discretizar el conjunto de estados. Y, para completar el modelo, es preciso discretizar el conjunto de puertas cuánticas, encontrar aproximaciones de puertas cuánticas generales por puertas discretas y encontrar, para el modelo discreto, conjuntos universales de puertas cuánticas. En este trabajo introducimos los conjuntos de estados y puertas cuánticas discretas, los caracterizamos, estudiamos sus propiedades más importantes y proponemos un conjunto finito de puertas que es universal.

**Quantum Simulation of Quantum Field Theories in Trapped Ions**

Jorge Casanova (UPV-EHU)

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.

**3-qubit entanglement: Complete measures, maximally entangled states and remote preparation of resources**

Julio de Vicente (Universitaet Innsbruck)

Whereas bipartite entanglement of pure states is well understood, multipartite entanglement is much more subtle. For instance, in the bipartite case there exists a unique maximally entangled state (MES) (in the sense that it can be transformed to any other state by deterministic local operations and classical communication (LOCC)), while in the multipartite case there are infinitely many. In fact, our understanding of the nonlocal properties of many-body states is far from complete even in the simplest case of just three subsystems. In this contribution, we characterize the entanglement contained in a pure 3–qubit state via operational entanglement measures. To this end we derive a new decomposition for arbitrary 3–qubit states, which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities, which are easily computable, characterize the different forms of bipartite entanglement required to generate the state following a particular preparation procedure and, hence, have a clear physical meaning. In addition to this, we show that the classification of states obtained in this way is strongly related to the one obtained when considering LOCC and that MES can be characterized by a simple condition in terms of our parameters. Moreover, our insights can be used to devise protocols in which a provider remotely prepares arbitrary (maximally) entangled states for spatially separated parties. These protocols are shown to efficient in terms of the quantum and classical communication that needs to be used to achieve them.

**Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions**

Lucas Lamata (UPV-EHU)

We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings. We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources. The proposed scheme can be relevant in a variety of fields such as condensed-matter or high-energy physics, where quantum simulations may solve problems intractable for classical computers.

J. Casanova, A. Mezzacapo, L. Lamata, and E. Solano, Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions, Phys. Rev. Lett. 108, 190502 (2012).

**Quantum Storage of a Photonic Polarization Qubit in a Solid**

Matteo Cristiani (ICFO)

The ability of mapping the quantum state of light onto matter in a coherent and reversible way is universally considered to be a fundamental tool in quantum information science. The precise control of the interaction between atoms and photons would enable the construction of efficient light-matter interfaces, which constitute a fundamental ingredient for the experimental realization of quantum memories (QM) for photons. During the past decades, numerous systems have been proposed for the experimental realization of photonic quantum memories. Among those, rare-earth doped crystals are promising candidates owing to their unique coherent properties. In particular, QMs based on praseodymium doped crystals displayed record storage time and high retrieval efficiency. However, due to the strong dependence of the absorption on the polarization state of light observed in such systems, the use of rare-earth doped crystals as quantum memories for polarization qubits is not straightforward. This is a main limitation, considering that quantum information is often encoded in the polarization degree of freedom of photons. In this work we overcome the problem of anisotropy by mapping the two components of the input polarization onto two spatially separated modes of the crystal. This allows us to observe quantum storage and retrieval of polarization qubits onto and out of a praseodymium based solid state storage device for the first time. The qubits are implemented with weak coherent states at the single photon level, and are stored for a pre-determined time of 500 ns with a storage and retrieval efficiency of 10 %, using the atomic frequency comb scheme. We characterize the storage by using quantum state tomography, and find that the average conditional fidelity of the retrieved qubits exceeds 95% for a mean photon number below 4. This is significantly higher than a classical benchmark which proves that our device functions as a quantum storage device for polarization qubits.

**Gauge theory, plaquette models and spin chains**

Miguel Tíerz (Univ. Complutense de Madrid)

We show how thermal correlation functions of spin chains are related to plaquette models of lattice gauge theory and how the observables of a number of low dimensional gauge theories can be reproduced by such correlation functions. We will emphasize the case of topological gauge theory.

**Thermal Stability of Topological Quantum Memories**

Oscar Viyuela García (Univ. Complutense de Madrid)

One promising candidate to implement fault-tolerant methods for quantum information processing are topological orders in strongly correlated systems. Using the quantum theory of open systems I will discuss their stability in the presence of thermal noise. Firstly, I will focus on topological quantum memories [1] and later I will show how to use these techniques to study how dynamical thermal effects attack topologically ordered systems in condensed matter such as topological insulators [2].

[1] O. Viyuela, A. Rivas, M.A. Martin-Delgado, Generalized Toric Codes Coupled to Thermal Baths. New J. Phys. 14 033044 (2012).

**Diﬀerential magnetometry with multiparticle singlets**

Philipp Hyllus (UPV-EHU)

We present a method for measuring the magnetic ﬁeld gradient with singlets realized with spin-1/2 particles. While the singlet state does not change under the inﬂuence of homogenous magnetic ﬁelds, the variance of the collective spin components starts to grow under a ﬁeld gradient. We compute the dynamics of this variance analytically for a chain of spins and also for an ensemble of particles with a given density distribution. We calculate an upper bound on how exactly the ﬁeld gradient can be estimated from the measured data. The proposal is relevant for cold atomic ensembles where multiparticle singlet states can be prepared by spin squeezing and diﬀerential magnetometry can be carried out.

**Enlace aéreo de QKD a alta velocidad en Madrid**

Veronica Fernandez (Instituto de Seguridad de la Información, CSIC)

Se ha diseñado, implementado experimentalmente y caracterizado un sistema de transmisión cuántica de clave (QKD) a alta velocidad a través del espacio libre para entorno urbano. El sistema utiliza dos láseres tipo VCSEL a una longitud de onda de 850 nm para transmitir la clave mediante el protocolo de transmisión cuántica de clave basado en polarización B92. Ambos láseres son modulados entre 1 GHz y 3 GHz de frecuencia reloj y son capaces de emitir a 4 Gbps. Un tercer láser a una longitud de 1550 nm se utiliza para transmitir la señal temporal de sincronizado entre emisor y receptor. El emisor va montado sobre un sistema gimbal de dos motores de alta precisión para proveer de los movimientos de ascensión recta y declinación necesarios para la alineación precisa con el receptor. El haz de salida de Alice es expandido y colimado por Alice a un tamaño de 4 cm de diámetro. El receptor del sistema de QKD cuenta con un telescopio Schmidt-Cassegrain de 25 cm de diámetro para focalizar eficientemente el haz que le llega de Alice. Los estados ‘0’ y ‘1’ que componen la clave son detectados por detectores de fotones individuales comerciales de Silicio. Una tarjeta de contado de alta precisión procesa los tiempos de llegada para permitir el análisis posterior del error del sistema y la tasa de clave segura transmitida. El sistema se ha caracterizado en pruebas preliminares entre dos laboratorios del Instituto de Seguridad de la Información a una distancia de 30m. Se transmitieron claves seguras a frecuencias reloj entre 1 GHz y 3 GHz en condiciones nocturnas, siendo la frecuencia óptima 1.5 GHz con un QBER de 2%, una sifted bit rate de 1.5 Mbit/s y una tasa segura de clave de 840 Kbits/s (un orden de magnitud superior a lo conseguido hasta el momento). En la tasa segura de bits se substrajeron los bits que Eve ha interceptado debido a pulsos emitidos con más de un fotón además de los bits publicados en corrección de errores y amplificación de privacidad. El sistema se caracterizó también en condiciones diurnas a la frecuencia óptima de1.5 GHz obteniéndose tasas seguras de bits en prácticamente la totalidad del día (98%). El enlace óptico se mantuvo estable durante 24h sin necesidad de realineación externa. El sistema está siendo actualmente trasladado a una distancia entre emisor y receptor de 300 m en el campus del CSIC de Serrano para la transmisión de claves seguras entre el Instituto de Seguridad de la Información y el Instituto de Ciencias Agrarias. La previsión es que el sistema se comporte de forma similar ya que la absorción atmosférica a 300 m es sólo un 10% superior a la de 30m, con lo que superaría considerablemente en velocidad a los sistemas realizados hasta la fecha.

**FROM CLASSICAL TO QUANTUM SYNCHRONIZATION**

Zambrini Roberta (IFISC, CSIC)

Synchronization has been largely studied in physical, biological and chemical classical systems and the aim of this talk is to present results in the quantum regime, looking for the quantum aspects of this phenomenon. We consider networks of detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to spontaneous synchronization and show the possibility to locally tune a network to achieve collective as well as partial synchronization. We find that this spontaneous phenomenon is accompanied by robust quantum discord and mutual information between the oscillators, preventing the leak of information from the system into the environment. Finally we discuss the possibility to bring two oscillators into an entangled state by proper coupling to a network.

**Non-Equilibrium Dynamics of Quantum Magnets**

Ángel Rivas (Univ. Complutense de Madrid)

We derive a master equation which allows us to study non-equilibrium dynamics of a quantum magnet. By resorting to spin wave theory we obtain a closed analytic form for the magnon decay rates. These turn out to be closely related to form factors, which are experimentally accessible by means of neutron and Raman scattering. We show that, for moderate temperatures, the magnetic order is not spoilt even if the coupling is fully isotropic. Remarkably, a decoherence free subspace arises for quantum antiferromagnets which is absent for ferromagnetic systems.

**Holography, Tensor Networks and correlations between distant regions at criticality**

Javier Molina (Universidad Politecnica de Cartagena)

Recently, it has been proposed that in (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d +2) holographic geometry of Anti de Sitter space (AdS) with the original system lying at the boundary. In this talk we analyze the MERA renormalization flow that arises when computing the correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition may be easily accounted by an AdS black hole geometry when the mutual information (MI) between the blocks is computed using the Ryu-Takayanagi formula. Our results for a 1D dimensional system, show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value and we discuss the robustness of this transition when finite size effects are taken into account.

## Poster

**Quantum optical signals in telecommunication networks**

Alex Ciurana Aguilar (Univ. Politécnica de Madrid)

In this work we discuss the integration of quantum optical signals into telecommunication networks. Nowadays, telecom networks tend to use optical components; this enables the transmission of qubits and, thus, the integration of quantum technologies. Moreover, this integration benefits both of them. On one hand, quantum technologies can take advantage of a deployed infrastructure in terms of costs, resources and market share. On the other, some drawbacks of telecom networks can be solved using quantum technologies. For instance, from a security standpoint, quantum key distribution can provide telecom networks with symmetric keys with information-theoretic security. In particular, we focus on telecom metropolitan optical networks based on wavelength-division multiplexing technology. This technology uses different wavelengths in order to transmit multiple signals simultaneously in the same fiber. Within this wavelengths grid, we study how to accommodate quantum signals beside conventional ones (typically 100 dB powerful) and how they should be routed using only passive optical components. There are two factors that hamper this integration and need to be tackled: noise sources (e.g., Raman scattering, four-wave mixing, crosstalk), because of the power difference; and the lack of practical wavelength-converters or amplifiers in the quantum regime.

**Heteronuclear magnetic molecular clusters for quantum computation**

Ana Repollés (ICMA-Unizar)

**Criticality, order parameters and Schmidt coefficients**

Anna Sanpera (ICREA / UAB)

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e. the difference between the two largest eigenvalues of the reduced density matrix $\lambda*{1},\lambda*$, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding conformal theory describing the critical point. Such scaling behavior allows to identify explicitly the Schmidt gap as a local order parameter.

**Detecting entanglement of two-electron spin qubits with witness operators**

Antoni Borràs (Universitat de les Illes Balears)

We propose a scheme for detecting entanglement between two-electron spin qubits in a double quantum dot using an entanglement witness operator. We first calculate the optimal configuration of the two electron spins, defined as the position in the energy level spectrum where, averaged over the nuclear spin distribution, (1) the probability to have two separated electrons and (2) the degree of entanglement of the quantum state quantified by the concurrence are both large. Using a density matrix approach, we then calculate the evolution of the expectation value of the witness operator for the two-spin singlet state, taking into account the effect of decoherence due to quantum charge fluctuations modeled as a boson bath. We find that, for large interdot coupling, it is possible to obtain a highly entangled and robust ground state.

**Reconciliación segura y adaptable**

David Elkouss Coronas (Univ. Politécnica de Madrid)

El problema de reconciliación de información en los protocolos de destilación de claves secretas puede ser modelado como un problema de codificación de fuente con información en el receptor. En consecuencia, se puede obtener métodos de reconciliación basados en códigos correctores de errores para canales con ruido. Sin embargo muchos códigos correctores de errores tienen una tasa fija de información. Recientemente se ha propuesto un protocolo que adapta la tasa de información con la ayuda de extensiones de la fuente original. En esta contribución mostramos que estas extensiones no comprometen la seguridad del proceso de destilación de claves y permiten una reconciliación altamente eficiente.

**Estudio teórico de trímeros de Tb3+ para su uso como espín qubits**

Jose Jaime Baldovi Jachan (ICMOL, Univ. Valencia)

En este estudio se presenta la caracterización teórica de los compuestos [{Tb(TETA)}2Tb(H2O)8]+, TETA = ácido 1,4,8,11-tetraazaciclotetradecano-1,4,8,11-tetraacético y Tb3Q9, Q=quinolinato, empleando un hamiltoniano efectivo de campo cristalino basado en un modelo de cargas puntuales efectivas. Como resultado se presentan los niveles de energía, las funciones de onda y, en base a éstos, la aplicación de dichos trímeros como espín qubits. En concreto, el estudio de estos sistemas está enfocado a su uso en computación cuántica con la implementación de la correción cuántica de errores de Shor.

**Design and fabrication of rf coplanar nanocavities for QED with magnetic molecular qubits**

Mark Jenkins (ICMA-Unizar)