@mastersthesis {294,
title = {Quantum Information with continuous variable systems},
volume = {PhD},
year = {2010},
month = {04/2010},
school = {Universitat Aut{\`o}noma de Barcelona},
type = {PhD Thesis},
address = {Barcelona},
abstract = {This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. CV systems are those described by canonical conjugated coordinates $x$ and $p$ endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. We present a protocol that permits to extract quantum keys from entangled Gaussian states. Differently from discrete systems, Gaussian entangled states cannot be distilled with Gaussian operations only. However it was already shown, that it is still possible to extract perfectly correlated classical bits to establish secret random keys. We properly modify the protocol using bipartite Gaussian entanglement to perform quantum key distribution in an efficient and realistic way. We describe and demonstrate security in front of different possible attacks on the communication, detailing the resources demanded. We also consider a simple 3-partite protocol known as Byzantine Agreement. It is an old classical communication problem in which parties (with possible traitors among them) can only communicate pairwise, while trying to reach a common decision. Classically, there is a bound in the maximal number of possible traitors that can be involved in the game. Nevertheless, a quantum solution exist. We show that solution within CV using multipartite entangled Gaussian states and Gaussian operations. Furthermore, we show under which premises concerning entanglement content of the state, noise, inefficient homodyne detectors, our protocol is efficient and applicable with present technology.
It is known that in spite of their exceptional role within the space of all CV states, in fact, Gaussian states are not always the best candidates to perform quantum information tasks. Thus, we tackle the problem of quantification of correlations (quantum and/or classical) between two CV modes (Gaussian and non-Gaussian). We propose to define correlations between the two modes as the maximal number of correlated bits extracted via local quadrature measurements on each mode. On Gaussian states, where entanglement is accessible via their covariance matrix our quantification majorizes entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon subtracted states and mixtures of Gaussian states, the bit quadrature correlations are shown to be also a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without needing a complete state tomography with the same complexity as if dealing with Gaussian states.
Finally we focus to atomic ensembles described as CV. Measurement induced entanglement between two macroscopical atomic samples was reported experimentally in 2001. There, the interaction between a single laser pulse propagating through two spatially separated atomic samples combined with a final projective measurement on the light led to the creation of pure EPR entanglement between the two samples. We show how to generate, manipulate and detect mesoscopic entanglement between an arbitrary number of atomic samples through a quantum non-demolition matter-light interface. Our proposal extends in a non-trivial way for multipartite entanglement (GHZ and cluster-like) without needing local magnetic fields. Moreover, we show quite surprisingly that given the irreversible character of a measurement, the interaction of the atomic sample with a second pulse light can modify and even reverse the entangling action of the first one leaving the samples in a separable state.},
author = {Rod{\'o}, Carles}
}
@article {Rodo2009,
title = {Manipulating mesoscopic multipartite entanglement with atom-light interfaces},
journal = {Physical Review A (Atomic, Molecular, and Optical Physics)},
volume = {80},
number = {6},
year = {2009},
month = {12/2009},
pages = {062304{\textendash}8},
publisher = {APS},
abstract = {Entanglementbetween two macroscopic atomic ensembles induced by measurement on anancillary light system has proven to be a powerful methodfor engineering quantum memories and quantum state transfer. Here weinvestigate the feasibility of such methods for generation, manipulation, anddetection of genuine multipartite entanglement (Greenberger-Horne-Zeilinger and clusterlike states) betweenmesoscopic atomic ensembles without the need of individual addressing ofthe samples. Our results extend in a nontrivial way theEinstein-Podolsky-Rosen entanglement between two macroscopic gas samples reported experimentally in[B. Julsgaard, A. Kozhekin, and E. Polzik, Nature (London) 413,400 (2001)]. We find that under realistic conditions, a secondorthogonal light pulse interacting with the atomic samples, can modifyand even reverse the entangling action of the first oneleaving the samples in a separable state. {\textcopyright}2009 The American Physical Society},
keywords = {atom-photon collisions, EPR paradox, measurement theory, mesoscopic entanglement, multipartite entanglement, quantum entanglement, quantum optics},
url = {http://link.aps.org/abstract/PRA/v80/e062304},
author = {Julia Stasi{\'n}ska and Rod{\'o}, Carles and Paganelli, Simone and Sanpera, Anna and Birkl, G.}
}
@article {Neigovzen2008,
title = {Multipartite continuous-variable solution for the Byzantine agreement problem},
journal = {Physical Review A (Atomic, Molecular, and Optical Physics)},
volume = {77},
number = {6},
year = {2008},
month = {06/2008},
pages = {062307{\textendash}11},
keywords = {Gaussian processes, homodyne detection, quantum cryptography, quantum entanglement},
doi = {10.1103/PhysRevA.77.062307},
url = {http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf\&id=PLRAAN000077000006062307000001\&idtype=cvips\&prog=normal},
author = {Neigovzen, Rodion and Rod{\'o}, Carles and Adesso, Gerardo and Sanpera, Anna}
}
@article {Rodo2008,
title = {Operational Quantification of Continuous-Variable Correlations},
journal = {Physical Review Letters},
volume = {100},
number = {11},
year = {2008},
month = {03/2008},
pages = {110505{\textendash}4},
doi = {10.1103/PhysRevLett.100.110505},
url = {http://link.aps.org/abstract/PRL/v100/e110505},
author = {Rod{\'o}, Carles and Adesso, Gerardo and Sanpera, Anna}
}
@article {Rodo2007,
title = {Efficiency in Quantum Key Distribution Protocols with Entangled Gaussian States},
journal = {Open Systems \& Information Dynamics},
volume = {14},
number = {1},
year = {2007},
month = {03/2007},
pages = {69{\textendash}80},
abstract = {Abstract Quantum key distribution (QKD) refers to specific quantum strategies which permit the secure distribution of a secret key between two parties that wish to communicate secretly. Quantum cryptography has proven unconditionally secure in ideal scenarios and has been successfully implemented using quantum states with finite (discrete) as well as infinite (continuous) degrees of freedom. Here, we analyze the efficiency of QKD protocols that use as a resource entangled gaussian states and gaussian operations only. In this framework, it has already been shown that QKD is possible [1] but the issue of its efficiency has not been considered. We propose a figure of merit (the efficiency E) to quantify the number of classical correlated bits that can be used to distill a key from a sample of N entangled states. We relate the efficiency of the protocol to the entanglement and purity of the states shared between the parties.},
keywords = {gaussian states, quantum cryptography, quantum key distribution},
doi = {10.1007/s11080-007-9030-x},
url = {http://dx.doi.org/10.1007/s11080-007-9030-x},
author = {Rod{\'o}, Carles and Romero-Isart, Oriol and Eckert, Kai and Sanpera, Anna}
}
@article {Romero-Isart2007,
title = {Transport and entanglement generation in the Bose-Hubbard model},
journal = {Journal of Physics A: Mathematical and General},
volume = {40},
number = {28},
year = {2007},
pages = {8019{\textendash}8032},
url = {http://www.iop.org/EJ/article/1751-8121/40/28/S11/a7\_28\_s11.pdf},
author = {Romero-Isart, Oriol and Eckert, Kai and Rod{\'o}, Carles and Sanpera, Anna}
}