04248nas a2200133 4500008003900000245005700039210005700096260005900153490000800212520375800220100001803978700001803996856010004014 2010 d00aQuantum Information with continuous variable systems0 aQuantum Information with continuous variable systems aBarcelonabUniversitat Autònoma de Barcelonac04/20100 vPhD3 aThis 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.1 aSanpera, Anna1 aRodó, Carles uhttps://grupsderecerca.uab.cat/giq/publications/quantum-information-continuous-variable-systems01755nas a2200265 4500008004100000245008100041210006900122260001700191300001500208490000700223520094900230653002701179653001601206653002301222653002801245653003001273653002501303653001901328100002201347700001801369700002201387700001801409700001301427856004901440 2009 eng d00aManipulating mesoscopic multipartite entanglement with atom-light interfaces0 aManipulating mesoscopic multipartite entanglement with atomlight bAPSc12/2009 a062304–80 v803 aEntanglementbetween 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. ©2009 The American Physical Society10aatom-photon collisions10aEPR paradox10ameasurement theory10amesoscopic entanglement10amultipartite entanglement10aquantum entanglement10aquantum optics1 aStasińska, Julia1 aRodó, Carles1 aPaganelli, Simone1 aSanpera, Anna1 aBirkl, G uhttp://link.aps.org/abstract/PRA/v80/e06230400737nas a2200205 4500008004100000245008200041210006900123260001200192300001600204490000700220653002300227653002300250653002500273653002500298100002200323700001800345700002000363700001800383856013000401 2008 eng d00aMultipartite continuous-variable solution for the Byzantine agreement problem0 aMultipartite continuousvariable solution for the Byzantine agree c06/2008 a062307–110 v7710aGaussian processes10ahomodyne detection10aquantum cryptography10aquantum entanglement1 aNeigovzen, Rodion1 aRodó, Carles1 aAdesso, Gerardo1 aSanpera, Anna uhttp://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PLRAAN000077000006062307000001&idtype=cvips&prog=normal00461nas a2200145 4500008004100000245006700041210006600108260001200174300001500186490000800201100001800209700002000227700001800247856005000265 2008 eng d00aOperational Quantification of Continuous-Variable Correlations0 aOperational Quantification of ContinuousVariable Correlations c03/2008 a110505–40 v1001 aRodó, Carles1 aAdesso, Gerardo1 aSanpera, Anna uhttp://link.aps.org/abstract/PRL/v100/e11050501568nas a2200205 4500008004100000245008400041210006900125260001200194300001200206490000700218520093900225653002001164653002501184653002901209100001801238700002401256700001601280700001801296856004801314 2007 eng d00aEfficiency in Quantum Key Distribution Protocols with Entangled Gaussian States0 aEfficiency in Quantum Key Distribution Protocols with Entangled c03/2007 a69–800 v143 aAbstract 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.10agaussian states10aquantum cryptography10aquantum key distribution1 aRodó, Carles1 aRomero-Isart, Oriol1 aEckert, Kai1 aSanpera, Anna uhttp://dx.doi.org/10.1007/s11080-007-9030-x00491nas a2200145 4500008004100000245006800041210006700109300001600176490000700192100002400199700001600223700001800239700001800257856007000275 2007 eng d00aTransport and entanglement generation in the Bose-Hubbard model0 aTransport and entanglement generation in the BoseHubbard model a8019–80320 v401 aRomero-Isart, Oriol1 aEckert, Kai1 aRodó, Carles1 aSanpera, Anna uhttp://www.iop.org/EJ/article/1751-8121/40/28/S11/a7\_28\_s11.pdf