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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Witnessing of Multipartite Entanglement

Jan Sperling, W. Vogel

Published Jan 1, 2013• 2 citations
Publisher

Abstract

We study the construction of witnesses for multipartite entanglement. This is done via the so-called multipartite separability eigenvalue equations. By its analytical solution, we identify high order multipartite entanglement in continuous variable systems.
DOI
10.1364/cqo.2013.m6.57

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This cumulative dissertation introduces new methods of the topic of entanglement testing based on the separability eigenvalue equations. In principle, the separability eigenvalue equations represent a method to construct entanglement tests via witnessing approaches. An approach is presented that enables finding reliable entanglement tests even for experimental states. A newly introduced algorithm, the Separability Power Iteration, enables finding solutions to the separability eigenvalue equations numerically, thereby broadening the range on the introduced approach.
Entanglement in multipartite systems is a key resource for quantum information and communication protocols, making its verification in complex systems a necessity.Because an exact calculation of arbitrary entanglement probes is impossible, we derive and implement a numerical method to construct multipartite witnesses to uncover entanglement in arbitrary systems.Our technique is based on a substantial generalization of the power iteration-an essential tool for computing eigenvalues-and it is a solver for the separability eigenvalue equations, enabling the general formulation of optimal entanglement witnesses.Beyond our rigorous derivation and direct implementation of this method, we apply our approach to several examples of complexly quantum-correlated states and benchmark its general performance.Consequently, we provide a generally applicable numerical tool for the identification of multipartite entanglement.
We study the problem of witnessing entanglement among indistinguishable particles. For this purpose, we derive a set of equations which results in necessary and sufficient conditions for probing multipartite entanglement between arbitrary systems of bosons or fermions. The solution of these equations yields the construction of optimal entanglement witnesses for partial and full entanglement in discrete and continuous variable systems. Our approach unifies the verification of entanglement for distinguishable and indistinguishable particles. We provide general solutions for certain observables to study quantum entanglement in systems with different quantum statistics in noisy environments.
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been entangled to build a quantum computer or a quantum simulator, theoretically only for lower dimensional quantum system such as two qubit system or two-mode Gaussian state and some special quantum states, efficient criteria have been developed to detect the entanglement. An efficient and practical entanglement detection method is anticipated to appear for current scalable quantum system. Based on the matched entanglement witness scheme and integrated uncertainty relations, we propose a quite general entanglement detection method for all kinds of multipartite entanglement of multimode continuous variable systems. With the covariance matrix of any randomly generated multimode continuous variable quantum state, our criterion can detect entanglement, genuine entanglement and other kinds of inseparabilities almost imidiately.
We establish a relation between entanglement of a many-body system and its diffractive properties, where the link is given by structure factors. Based on these, we provide a general analytical construction of multiqubit entanglement witnesses. The proposed witnesses contain two-point correlations. They could be either measured in a scattering experiment or via local measurements, depending on the underlying physical system. For some explicit examples of witnesses we analyze the properties of the states that are detected by them. We further study the robustness of these witnesses with respect to noise.