Efficient quantum state analysis and entanglement detection

Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.Verschränkung ist eines der grundlegendsten Phänomene der Quantentheorie und lässt sich nur unzureichend durch einen klassischen Formalismus beschreiben. Verschränkung spielt nicht nur möglicherweise eine Rolle in natürlichen Prozessen, sondern stellt insbesondere eine sehr mächtige Ressource für eine Vielzahl an Anwendungen bereit. So beruhen Quanteninformationsprotokolle wie Quantenzustandsteleportation, superdense coding sowie diverse Ansätze für quantum computation darauf. Dennoch ist es gerade in größeren Systemen, die aus mehr als zwei Teilchen bestehen, äußerst schwierig, Verschränkung nachzuweisen. In der hier vorliegenden Arbeit werden verschiedene Methoden vorgestellt, mit denen Vielteilchenverschränkung effizient detektiert werden kann. Diese Methoden werden experimentell untersucht und anschließend in Hinblick auf ihre Verwendbarkeit diskutiert. Darüber hinaus werden Methoden für Quantenzustands- und Quantenprozesstomographie eingeführt, mit deren Hilfe experimentelle Aufbauten genauestens untersucht werden können. Die dabei typischen Herausforderungen werden aufgezeigt, wobei Methoden präsentiert werden, die neue Einblicke in experimentell gewonnene Daten erlauben. Abschließend wird das sogenannte Messproblem beleuchtet, das die unvermeidbare Störung eines Quantensystems durch einen Messprozess beschreibt. Es werden verschiedene Methoden für Quantenmessungen diskutiert, wobei schließlich die optimalen Messinstrumente hergeleitet werden. Mit diesen kann Information über einen Zustand gewonnen werden, während die dadurch verursachte Störung gleichzeitig minimiert wird. Diese optimalen Instrumente werden mit anderen Messschemata verglichen, die beispielsweise auf dem optimalen Quantenkloner beruhen

Optimized state independent entanglement detection based on geometrical threshold criterion

Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation complementarity. Our first scheme essentially establishes the Schmidt decomposition for pure states, with few measurements only and without the need for shared reference frames. The second scheme employs a decision tree to speed up entanglement detection. We analyze the performance of the methods using numerical simulations and verify them experimentally for various states of two, three and four qubits.Comment: 13 pages, 12 figure

Efficient quantum state analysis and entanglement detection

Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.Verschränkung ist eines der grundlegendsten Phänomene der Quantentheorie und lässt sich nur unzureichend durch einen klassischen Formalismus beschreiben. Verschränkung spielt nicht nur möglicherweise eine Rolle in natürlichen Prozessen, sondern stellt insbesondere eine sehr mächtige Ressource für eine Vielzahl an Anwendungen bereit. So beruhen Quanteninformationsprotokolle wie Quantenzustandsteleportation, superdense coding sowie diverse Ansätze für quantum computation darauf. Dennoch ist es gerade in größeren Systemen, die aus mehr als zwei Teilchen bestehen, äußerst schwierig, Verschränkung nachzuweisen. In der hier vorliegenden Arbeit werden verschiedene Methoden vorgestellt, mit denen Vielteilchenverschränkung effizient detektiert werden kann. Diese Methoden werden experimentell untersucht und anschließend in Hinblick auf ihre Verwendbarkeit diskutiert. Darüber hinaus werden Methoden für Quantenzustands- und Quantenprozesstomographie eingeführt, mit deren Hilfe experimentelle Aufbauten genauestens untersucht werden können. Die dabei typischen Herausforderungen werden aufgezeigt, wobei Methoden präsentiert werden, die neue Einblicke in experimentell gewonnene Daten erlauben. Abschließend wird das sogenannte Messproblem beleuchtet, das die unvermeidbare Störung eines Quantensystems durch einen Messprozess beschreibt. Es werden verschiedene Methoden für Quantenmessungen diskutiert, wobei schließlich die optimalen Messinstrumente hergeleitet werden. Mit diesen kann Information über einen Zustand gewonnen werden, während die dadurch verursachte Störung gleichzeitig minimiert wird. Diese optimalen Instrumente werden mit anderen Messschemata verglichen, die beispielsweise auf dem optimalen Quantenkloner beruhen

Systematic errors in current quantum state tomography tools

Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we observe a systematic underestimation of the fidelity and an overestimation of entanglement. A solution for this problem can be achieved by a linear evaluation of the data yielding reliable and computational simple bounds including error bars.Comment: 8 pages, 8 figure

An Improved Experiment to Determine the `Past of a Particle' in the Nested Mach-Zehnder Interferometer

We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32, 050303 (2015)] to the experiment of Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] does not test the past of the photon as characterised by local weak traces. Instead of answering the questions: (i) Were the photons in A? (ii) Were the photons in B? (iii) Were the photons in C? the proposed experiment measures a degenerate operator answering the questions: (i) Were the photons in A? (ii) Were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. A simple variation of the modified experiment does provide good evidence for the past of the photon in agreement with the results Danan et al. obtained.Comment: 3 pages, accepted for publication in Chinese Physics Letter

Gaussian state entanglement witnessing through lossy compression

We propose a method to witness entanglement between two continuous-variable systems in a Gaussian state. Its key ingredient is a local lossy state transfer from the original spatially separated systems onto two spatially separated qubits. The qubits are initially in a pure product state, therefore by detecting entanglement between the qubits we witness entanglement between the two original systems. This method greatly simplifies entanglement witnessing in complex systems.Comment: 5 pages, 2 figure

Deep-Learning-Based Radio-Frequency Side-Channel Attack on Quantum Key Distribution

Quantum key distribution (QKD) protocols are proven secure based on fundamental physical laws, however, the proofs consider a well-defined setting and encoding of the sent quantum signals only. Side channels, where the encoded quantum state is correlated with properties of other degrees of freedom of the quantum channel, allow an eavesdropper to obtain information unnoticeably as demonstrated in a number of hacking attacks on the quantum channel. Yet, also classical radiation emitted by the devices may be correlated, leaking information on the potential key, especially when combined with novel data analysis methods. We here demonstrate a side-channel attack using a deep convolutional neural network to analyze the recorded classical, radio-frequency electromagnetic emissions. Even at a distance of a few centimeters from the electronics of a QKD sender employing frequently used electronic components we are able to recover virtually all information about the secret key. Yet, as shown here, countermeasures can enable a significant reduction of both the emissions and the amount of secret key information leaked to the attacker. Our analysis methods are independent of the actual device and thus provide a starting point for assessing the presence of classical side channels in QKD devices.Comment: 14 pages, 10 figures. Comments welcome

High validity entanglement verification with finite copies of a quantum state

Detecting entanglement of multipartite quantum states is an inherently probabilistic process due to a finite number of measured samples. The level of confidence of entanglement detection can be used to quantify the probability that the measured signal is coming from a separable state and provides a meaningful figure of merit for big data sets. Yet, for limited sample sizes, to avoid serious misinterpretations of the experimental results, one should not only consider the probability that a separable state gave rise to the measured signal, but should also include information about the probability that the signal came from an entangled state. We demonstrate this explicitly and propose a comprehensive method of entanglement detection when only a very limited amount of data is available. The method is based on a non-linear combination of correlation functions and is independent of system size. As an example, we derive the optimal number of measurement settings and clicks per setting revealing entanglement with only 20 copies of a state.Comment: 13 pages, 4 figure