The study of Gaussian states has arisen to a privileged position in continuous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In this article, we provide a brief, and hopefully didactic, exposition of Gaussian state quantum information and its contemporary uses, including sometimes omitted crucial details. After introducing the subject material and outlining the essential toolbox of continuous variable systems, we define the basic notions needed to understand Gaussian states and Gaussian operations. In particular, emphasis is placed on the mathematical structure combining notions of algebra and symplectic geometry fundamental to a complete understanding of Gaussian informatics. Furthermore, we discuss the quantification of different forms of correlations (including entanglement and quantum discord) for Gaussian states, paying special attention to recently developed measures. The manuscript is concluded by succinctly expressing the main Gaussian state limitations and outlining a selection of possible future lines for quantum information processing with continuous variable systems.

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible. Steering is the quantum mechanical phenomenon that allows one party, Alice, to change (i.e., to "steer") the state of a distant party, Bob, by exploiting their shared entanglement. This phenomenon, fascinatingly discussed by Schrödinger [8,9], was already noted by Einstein, Podolksy, and Rosen (EPR) in their famous 1935 paper [12], and is at the heart of the so-called EPR paradox [13]. There it was argued that steering implied an unacceptable "action at a distance," which led EPR to claim the incompleteness of quantum theory. The EPR expectations for local realism were mostly extinguished by Bell's theorems [14,15], which showed that no locally causal theory can reproduce all the correlations observed in nature [16]. The first experimental criterion for the demonstration of the EPR paradox, i.e., for the detection of quantum steering, was later proposed by Reid [17], but it was not until 2007 that the particular type of nonlocality captured by the concept of steering [8,9,12] was in fact formalized [10,18].From a quantum information perspective [10], steering corresponds to the task of verifiable entanglement distribution by an untrusted party. If Alice and Bob share a state which is steerable in one way, say from Alice to Bob, then Alice is able to convince Bob (who does not trust Alice) that their shared state is entangled, by performing local measurements and classical communication [10]. Notice that steering, unlike entanglement, is an asymmetric property: a quantum state may be steerable from Alice to Bob, but not vice versa. On the operational side, it has been recently realized that steering provides security in one-sided device-independent quantum key distribution (QKD) [19], where the measurement apparatus of one party only is untrusted. These protocols are less demanding than totally device-independent ones, for which Bell nonlocality is known to be necessary [3]. Experimentally, at variance with the case of Bell tests, a demonstration of steering free of detection and locality loopholes is in reach [19][20][21][22], which makes one-sided device-independent QKD appealing for current technology and quantum steering a practically useful concept. EPR ste...

We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped with a notion of subsystems in the absence of a global tensor product structure. We argue that any apparent similarities between fermionic modes and qubits are superficial and can only be applied in limited situations. In particular, we discuss the ambiguities that arise from different treatments of this subject. Our results are independent of the specific context of the fermionic fields as long as the canonical anticommutation relations are satisfied, e.g., in relativistic quantum fields or fermionic trapped ions. * pmxnf@nottingham.ac.uk

The techniques employed to solve the interaction of a detector and a quantum field commonly require perturbative methods. We introduce mathematical techniques to solve the time evolution of an arbitrary number of detectors interacting with a quantum field moving in space-time while using non-perturbative methods. Our techniques apply to harmonic oscillator detectors and can be generalised to treat detectors modelled by quantum fields. Since the interaction Hamiltonian we introduce is quadratic in creation and annihilation operators, we are able to draw from continuous variable techniques commonly employed in quantum optics.

We study the effects of relativistic motion on quantum teleportation and propose a realizable experiment where our results can be tested. We compute bounds on the optimal fidelity of teleportation when one of the observers undergoes non-uniform motion for a finite time. The upper bound to the optimal fidelity is degraded due to the observer's motion however, we discuss how this degradation can be corrected. These effects are observable for experimental parameters that are within reach of cutting-edge superconducting technology. Our setup will further provide guidance for future space-based experiments.Comment: 5 pages, 4 figures, minor deviations from published version. I.F. previously published as Ivette Fuentes-Guridi and Ivette Fuentes-Schulle