The verification of experimentally created entanglement, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local measurements the measurement data will exhibit correlations, whether these systems are classical or quantum. Therefore, the observation of correlations in the classical measurement record does not automatically imply the presence of quantum correlations in the system under investigation. In this work we explore the question when correlations are sufficient to guarantee the existence of quantum correlations in the system and when additional information is needed to do so, such as the degree of purity of the system. Various measurement settings are discussed, both numerically and analytically. Exact results and lower bounds on the least entanglement consistent with the observations are presented. The approach is suitable both for the bi-partite and the multi-partite setting.
The verification of experimentally created entanglement, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local measurements the measurement data will exhibit correlations, whether these systems are classical or quantum. Therefore, the observation of correlations in the classical measurement record does not automatically imply the presence of quantum correlations in the system under investigation. In this work we explore the question when correlations are sufficient to guarantee the existence of quantum correlations in the system and when additional information is needed to do so, such as the degree of purity of the system. Various measurement settings are discussed, both numerically and analytically. Exact results and lower bounds on the least entanglement consistent with the observations are presented. The approach is suitable both for the bi-partite and the multi-partite setting.
The verification and quantification of experimentally created entanglement by simple measurements, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local measurements the measurement data will exhibit correlations, whether these systems are classical or quantum. Therefore, the observation of correlations in the classical measurement record does not automatically imply the presence of quantum correlations in the system under investigation. In this study, we explore the question of when correlations, or other measurement data, are sufficient to guarantee the existence of a certain amount of quantum correlations in the system and when additional information, such as the degree of purity of the system, is needed to do so. Various measurement settings are discussed, both numerically and analytically. Exact results and lower bounds on the least entanglement consistent with the observations are presented. The approach is suitable both for the bi-partite and the multi-partite setting.
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.
Entanglement does not describe all quantum correlations and several authors have shown the need to go beyond entanglement when dealing with mixed states. Various different measures have sprung up in the literature, for a variety of reasons, to describe bipartite and multipartite quantum correlations; some are known under the collective name {\it quantum discord}. Yet, in the same sprit as the criteria for entanglement measures, there is no general mechanism that determines whether a measure of quantum and classical correlations is a proper measure of correlations. This is partially due to the fact that the answer is a bit muddy. In this article we attempt tackle this muddy topic by writing down several criteria for a ``good" measure of correlations. We breakup our list into \emph{necessary}, \emph{reasonable}, and \emph{debatable} conditions. We then proceed to prove several of these conditions for generalized measures of quantum correlations. However, not all conditions are met by all measures; we show this via several examples. The reasonable conditions are related to continuity of correlations, which has not been previously discussed. Continuity is an important quality if one wants to probe quantum correlations in the laboratory. We show that most types of quantum discord are continuous but none are continuous with respect to the measurement basis used for optimization.
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires the determination of a parameter set that is growing exponentially with the number of qubits and becomes infeasible even for moderate numbers of particles. Non-trivial bounds on experimentally prepared entanglement can however be obtained from partial information on the density matrix. As introduced in the paper of K.M.R. Audenaert and M.B. Plenio [New J. Phys. 2006, 8, 266], the fundamental question is then formulated as: What is the entanglement content of the least entangled quantum state that is compatible with the available measurement data? We formulate the problem mathematically [Audenaert, K.M.R.; Plenio, M.B. New J. Phys. 2006, 8, 266] employing methods from the theory of semi-definite programming and then address this problem for the case, where the goal of the experiment is the creation of graph states. The observables that we consider are the generators of the stabilizer group, thus the number of measurement settings grows only linearly in the number of qubits. We provide analytical solutions as well as numerical methods that may be applied directly to experiments, and compare the obtained bounds with results from full-state tomography for simulated data.
Abstract Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states. We focus on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.
The paper presents an experiment that is a conceptual replication of two earlier experiments which demonstrate entanglement correlations between a quantum physical random process and certain psychological variables of human observers. In the present study button‐pushes were used as psychological variables. The button‐pushes were performed by the subject with his or her left or right hand in order to “control” (according to the instruction) a random process that could be observed on a display. Each button‐push started the next random event which, however, in reality, was independent of the button‐pushes. The study consists of three independent sets of data (n = 386) that were gained with almost fee same apparatus in three different experimental situations. The first data set serves as reference. It was an automatic control‐run without subjects. The second set was produced mainly by subjects who asked for taking part in a para‐psychological experiment and who visited the “Parapsychological Counseling Office” in Freiburg especially for this purpose. Most of them were highly motivated persons who wanted to test their “psi ability”. In this case the number of runs could be selected by the subjects before the experimental session. The third set of data (of the same size) was collected during two public exhibitions (at Basel and at Freiburg) where the visitors had the opportunity to participate in a “PK experiment”. In this case the number of trials and runs was fixed in advance, but the duration of the experiment was dependent of the speed of button‐pushes. The results corroborate the previous studies. The specific way how the subjects pushed the buttons is highly significantly correlated with the independent random process. This correlation shows up for the momentarily generated random events as well as for the previous and the later runs during the experimental session. In a strict sense, only the correlations with the future random events can be interpreted as non‐local correlations. The structure of the data, however, allows the conclusion, that all observed correlations can be considered as entanglement‐correlations. The number of entanglement‐correlations was significantly higher for the highly motivated group (data set 2) than for the unselected group of the exhibition participants (data set 3). The latter, however, where not completely unsuccessful: A subgroup who showed “innovative” behavior also showed significant entanglement‐correlations. It could further be shown, that the structure of the matrix of entanglement‐correlations is not stable in time and changes if the experiment is repeated. In comparison with previous correlation‐experiments, no decline of the effect size was observed. These results are in agreement with the predictions of the “Weak Quantum Theory (WQT)” and the “Model of Pragmatic Information (MPI)”. These models interpret the measured correlations as entanglement‐correlations within a self‐organizing, organizationally closed, psycho‐physical system that exist during a certain time‐interval (as long as the system is active). The entanglement‐correlations cannot be considered as a causal influence (in the sense of a PK‐Influence) and thus are called “micro‐synchronicity”. After a short introduction (1.), the question is discussed how non‐local correlations can be created in psycho‐physical systems (2.). In chapter (3.) the description of the experimental setting is given and the apparatus (4.) and randomness test of the random event generator (5.) are described. Additionally, an overview of the structure of the data is given (6.) and the analysis methods are described (7.). In chapter (8.) the experimental hypotheses are formulated and the results are reported (9.). After the discussion of the results (10.) the conclusions (11).) of the study are presented.