An operational interpretation for multipartite entanglement

We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation. We show that the estimation of the strength of low-noise locally depolarizing channels, as quantified by the regularized quantum Fisher information, is directly related to the Meyer-Wallach multipartite entanglement measure. Using channels that depolarize across different partitions, we obtain related multipartite entanglement measures. We show that this measure is the sum of expectation values of local observables on two copies of the state.Comment: 4 pages, 1 figur

Quantum entanglement

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended) presentation, updated references, minor changes, submitted to Rev. Mod. Phys

Correlations, Bell Inequality Violation & Quantum Entanglement

It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation.Comment: PhD Thesis (176 pages). This thesis contains (1) a pedagogical review of the field (2) results previously reported in quant-ph/0604045, quant-ph/0608128, quant-ph/0703268, arXiv:0710.5350 (3) some relevant details omitted from these publications (4) a formal proof of equivalence between the class of CGLMP inequalities and the I_{22dd} inequalitie

Efficient verification of universal and intermediate quantum computing

The promise of scalable quantum technology appears more realistic, after recent advances in both theory and experiment. Assuming a quantum computer is developed, the task of verifying the correctness of its outcome becomes crucial. Unfortunately, for a system that involves many particles, predicting its evolution via classical simulation becomes intractable. Moreover, verification of the outcome by computational methods, i.e. involving a classical witness, is believed inefficient for the hardest problems solvable by a quantum computer. A feasible alternative to verify quantum computation is via cryptographic methods, where an untrusted prover has to convince a weak verifier for the correctness of his outcome. This is the approach we take in this thesis. In the most standard configuration the prover is capable of computing all polynomial-time quantum circuits and the verifier is restricted to classical with very modest quantum power. The goal of existing verification protocols is to reduce the quantum requirements for the verifier - ideally making it purely classical - and reduce the communication complexity. In Part II we propose a composition of two existing verification protocols [Fitzsimons and Kashefi, 2012], [Aharonov et al., 2010] that achieves quadratic improvement in communication complexity, while keeping the quantum requirements for the verifier modest. Along this result, several new techniques are proposed, including the generalization of [Fitzsimons and Kashefi, 2012] to prime dimensions. In Part III we discuss the idea of model-specific quantum verification, where the prover is restricted to intermediate quantum power, i.e. between full-fledged quantum and purely classical, thus more feasible experimentally. As a proof of principle we propose a verification protocol for the One-Pure-Qubit computer [Knill and Laflamme, 1998], which tolerates noise and is capable of computing hard problems such as large matrix trace estimation. The verification protocol is an adaptation of [Fitzsimons and Kashefi, 2012] running on Measurement-Based Quantum Computing with newly proved properties of the underlying resources. Connections of quantum verification to other security primitives are considered in Part IV. Authenticated quantum communication has been already proved to relate to quantum verification. We expand this by proposing a quantum authentication protocol derived from [Fitzsimons and Kashefi, 2012] and discuss implications to verification with purely classical verifier. Connections between quantum security primitives, namely blindness - prover does not learn the computation -, and classical security are considered in Part V. We introduce a protocol where a client with restricted classical resources computes blindly a universal classical gate with the help of an untrusted server, by adding modest quantum capabilities to both client and server. This example of quantum-enhanced classical security we prove to be a task classically impossible

Proceedings of the 2019 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory

In 2019 fand wieder der jährliche Workshop des Fraunhofer IOSB und des Lehrstuhls für Interaktive Echtzeitsysteme des Karlsruher Insitut für Technologie statt. Die Doktoranden beider Institutionen präsentierten den Fortschritt ihrer Forschung in den Themen Maschinelles Lernen, Machine Vision, Messtechnik, Netzwerksicherheit und Usage Control. Die Ideen dieses Workshops sind in diesem Buch gesammelt in der Form technischer Berichte

On the Orthogonal Vector Problem and the Feasibility of Unconditionally Secure Leakage-Resilient Computation

We consider unconditionally secure leakage resilient two-party computation, where security means that the leakage obtained by an adversary can be simulated using a similar amount of leakage from the private inputs or outputs. A related problem is known as circuit compilation, where there is only one device doing a computation on public input and output. Here the goal is to ensure that the adversary learns only the input/output behaviour of the computation, even given leakage from the internal state of the device. We study these problems in an enhanced version of the ``only computation leaks\u27\u27 model, where the adversary is additionally allowed a bounded amount of {\em global} leakage from the state of the entity under attack. In this model, we show the first unconditionally secure leakage resilient two-party computation protocol. The protocol assumes access to correlated randomness in the form of a functionality \fOrt that outputs pairs of orthogonal vectors $(\vec{u}, \vec{v})$ over some finite field, where the adversary can leak independently from $\vec{u}$ and from $\vec{v}$. We also construct a general circuit compiler secure in the same leakage model. Our constructions work, even if the adversary is allowed to corrupt a constant fraction of the calls to \fOrt and decide which vectors should be output. On the negative side, we show that unconditionally secure two-party computation and circuit compilation are in general impossible in the plain version of our model. For circuit compilation we need a computational assumption to exhibit a function that cannot be securely computed, on the other hand impossibility holds even if global leakage is not allowed. It follows that even a somewhat unreliable version of \fOrt cannot be implemented with unconditional security in the plain leakage model, using classical communication. However, we show that an implementation using quantum communication does exist. In particular, we propose a simple ``prepare-and-measure\u27\u27 type protocol which we show secure using a new result on sampling from a quantum population. Although the protocol may produce a small number of incorrect pairs, this is sufficient for leakage resilient computation by our other results