We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory, and a lower bound to the entanglement can be read off directly from the scattering cross section of neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full characterization of the state to quantify the entanglement contained in it. Instead, the scheme presented here relies solely on global measurements that are routinely performed and is versatile enough to accommodate systems and measurements different from the ones we exemplify in this work.
We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory, and a lower bound to the entanglement can be read off directly from the scattering cross section of neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full characterization of the state to quantify the entanglement contained in it. Instead, the scheme presented here relies solely on global measurements that are routinely performed and is versatile enough to accommodate systems and measurements different from the ones we exemplify in this work.
Quantum entanglement has been identified as a crucial concept underlying many intriguing phenomena in condensed matter systems, such as topological phases or many-body localization.Recently, instead of considering mere quantifiers of entanglement such as entanglement entropy, the study of entanglement structure in terms of the entanglement spectrum has shifted to a focus leading to new insights into fractional quantum Hall states and topological insulators, among others.What remains a challenge is the experimental detection of such fine-grained properties of quantum systems.The development of protocols for detecting features of the entanglement spectrum in cold-atom systems, which are one of the leading platforms for quantum simulation, is thus highly desirable and will open up new avenues for experimentally exploring quantum many-body physics.Here, we present a method to bound the width of the entanglement spectrum, or entanglement dimension, of cold atoms in lattice geometries, requiring only measurements in two experimentally accessible bases and utilizing ballistic time-of-flight (TOF) expansion.Building on previous proposals for entanglement certification for photon pairs, we first consider entanglement between two atoms of different atomic species and later generalize to higher numbers of atoms per species and multispecies configurations showing multipartite high-dimensional entanglement.Through numerical simulations, we show that our method is robust against typical experimental noise effects and thus will enable high-dimensional entanglement certification in systems of up to eight atoms using currently available experimental techniques.
Abstract Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and it may require demanding tomographical techniques. Here, we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our framework provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N are required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for quantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups.
We demonstrate that two well-established experimental techniques of condensed-matter physics, neutron-diffraction scattering and measurement of magnetic susceptibility, can be used to detect and quantify macroscopic entanglement in solids. Specifically, magnetic susceptibility of copper nitrate (CN) measured in 1963 cannot be described without presence of entanglement. A detailed analysis of the spin correlations in CN as obtained from neutron-scattering experiment from 2000 provides microscopic support for this interpretation and gives the value for the amount of entanglement. We present a quantitative analysis resulting in the critical temperature of 5 K in both, completely independent, experiments below which entanglement exists.
In this thesis we present methods to efficiently verify quantum many-body experiments. The first part focuses on the quantitative verification of graph state experiments from simple measurements. In particular, optimal bounds on the fidelity, purity and entropy from stabilizer measurements are derived as well as high-quality bounds on entanglement measures. Furthermore, we show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory, and a lower bound to the entanglement can be read off directly from the scattering cross section of neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. Quantum mechanics offers many interesting properties such as entanglement and non-locality. However, one can easily think of more general correlations than quantum correlations. This gives rise to the question if quantum correlations are the most general allowed in nature? In the last part we propose a new axiom we call macroscopic locality. The idea behind this axiom is that any physical theory should recover classical physics in the continuum limit (i.e., when a large number of particles is involved and our measurement devices fail to resolve discrete particles). We will show that this very intuitive axiom, together with the no-signaling principle, allows to recover many important results in quantum mechanics, like the universality of the Tsirelson bound, or the set of accessible two-point correlators. Moreover, we will provide a complete characterization of the correlations between two distant physical systems that arise out of both axioms and comment on its consistency.
We show how the entanglement contained in states of spins arranged on a lattice may be lower bounded with observables arising in scattering experiments. We focus on the partial differential cross section obtained in neutron scattering from magnetic materials but our results are sufficiently general such that they may also be applied to, e.g., optical Bragg scattering from ultracold atoms in optical lattices or from ion chains. We discuss resonating valence bond states and ground and thermal states of experimentally relevant models---such as the Heisenberg, Majumdar-Ghosh, and XY models---in different geometries and with different spin numbers. As a by-product, we find that for the one-dimensional XY model in a transverse field such measurements reveal factorization and the quantum phase transition at zero temperature.
Entanglement is a fundamental resource for quantum information processing [1-3], its applications including scalable quantum communication, secure quantum key distribution protocols for cryptography, and exponential speedup of quantum algorithms. It occurs naturally in manybody systems at low temperatures: This makes cold atoms good candidates to provide entangled states involving a large number of particles. For realizing and manipulating such states, an essential task is quantifying the actual amount of entanglement contained in the created state before using it for quantum information protocols. However, this task represents a major challenge, as it requires either full state tomography, scaling exponentially in the system size, or the assumption of unverified system characteristics such as its Hamiltonian or temperature. In this experiment [4], we obtain a quantification of multipartite entanglement from readily accessible measurements - that is, time-of-flight atomic density distribution - based on a recent proposal [5]. We directly observe and quantify the multipartite spatial entanglement between the sites of a periodic optical potential (optical lattice) that hosts massive bosonic particles. We characterize its behaviour when crossing the superfluid-Mott insulator transition and when varying temperature, demonstrating the robustness of our method. References [1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (Cambridge, 2000). [2]R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865-942 (2009). [3]O. Göhne and G. Tóth, Entanglement detection, Physics Reports 474, 1-75 (2009). [4]M. Cramer, A. Bernard, N. Fabbri, L. Fallani, C. Fort, S. Rosi, F. Caruso, M. Inguscio, and M. B. Plenio, Entanglement of bosons in optical lattices, E-print arXiv:1302.4897 [5]M. Cramer, M. B. Plenio, and H. Wunderlich, Measuring entanglement in condensed matter systems, Phys. Rev. Lett. 106, 020401 (2011).