Large-Alphabet Time-Frequency Entangled Quantum Key Distribution by means of Time-to-Frequency Conversion

We introduce a novel time-frequency quantum key distribution (TFQKD) scheme based on photon pairs entangled in these two conjugate degrees of freedom. The scheme uses spectral detection and phase modulation to enable measurements in the temporal basis by means of time-to-frequency conversion. This allows large-alphabet encoding to be implemented with realistic components. A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size.Comment: 14 pages, 3 figures, submitte

Area laws for the entanglement entropy - a review

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: The entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium we review the current status of area laws in these fields. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation, and disordered systems, non-equilibrium situations, classical correlation concepts, and topological entanglement entropies are discussed. A significant proportion of the article is devoted to the quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. We discuss matrix-product states, higher-dimensional analogues, and states from entanglement renormalization and conclude by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations.Comment: 28 pages, 2 figures, final versio

Shaping frequency entangled qudits

Quantum entanglement between qudits - the d-dimensional version of qubits - is relevant for advanced quantum information processing and provides deeper insights in the nature of quantum correlations. Encoding qudits in the frequency modes of photon pairs produced by continuous parametric down-conversion enables access to high-dimensional states. By shaping the energy spectrum of entangled photons, we demonstrate the creation, characterization and manipulation of entangled qudits with dimension up to 4. Their respective density matrices are reconstructed by quantum state tomography. For qubits and qutrits we additionally measured the dependency of a d-dimensional Bell parameter for various degrees of entanglement. Our experiment demonstrates the ability to investigate the physics of high-dimensional frequency entangled qu$d$it states which are of great importance for quantum information science.Comment: 17 pages, 3 figure

Entanglement in Many-Body Systems

The recent interest in aspects common to quantum information and condensed matter has prompted a prosperous activity at the border of these disciplines that were far distant until few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermionic and bosonic model systems. Both bipartite and multipartite entanglement will be considered. At equilibrium we emphasize on how entanglement is connected to the phase diagram of the underlying model. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.Comment: 61 pages, 29 figure

Many-body localization dynamics from gauge invariance

We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, Gauss law effectively induces a dynamics which can be described as a disorder average over gauge super-selection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow entanglement growth are present in a broad regime of parameters - in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ions experiments realizing dynamical gauge fields, and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.Comment: 5Pages + appendices; V2: updated discussion in page 2, more numerical results, added reference