Quantum Information with continuous variable systems

TitleQuantum Information with continuous variable systems
Publication TypeThesis
Year of Publication2010
AuthorsRodó, C
AdvisorSanpera, A
Academic DepartmentDepartament de Físca, Grup de Física Teòria: Informació i fenòmens quàntics
Date Published04/2010
UniversityUniversitat Autònoma de Barcelona
Thesis TypePhD Thesis

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.

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