Nikolai WyderkaPhD student
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See also arxiv
Mariami Gachechiladze, Nikolai Wyderka and Otfried Gühne
Rigorous results on ultrafine entanglement witnesses
An entanglement witness is an observable with the property that a negative expectation value signals the presence of entanglement. The question arises how a witness can be improved if the expectation value of a second observable is known, and methods for doing this have recently been discussed as so-called ultrafine entanglement witnesses. We present several results on the characterization of entanglement given the expectation values of two observables. First, we explain that this problem can naturally be tackled with the method of the Legendre transformation, leading even to a quantification of entanglement. Second, we present necessary and sufficient conditions that two product observables are able to detect entanglement. Finally, we explain some fallacies in the original construction of ultrafine entanglement witnesses [F. Shahandeh et al., Phys. Rev. Lett. 118, 110502 (2017)].
Nikolai Wyderka, Felix Huber and Otfried Gühne
Constraints on correlations in qubit systems
In multiparticle quantum systems correlations can arise between different sets of particles. A possible strategy is to divide the global correlations into two components, depending on the question whether they affect an odd or an even number of particles. For pure multi-qubit states we prove that these two components are inextricably interwoven and often one type of correlations completely determines the other. As an application, we prove that all pure qubit states with an odd number of qubits are uniquely determined among all mixed states by the odd component of the correlations. In addition, our approach leads to invariants under the time evolution with Hamiltonians containing only odd correlations and can simplify entanglement detection.
We show that generic pure states (states drawn according to the Haar measure) of four particles of equal internal dimension are uniquely determined among all other pure states by their two-body marginals. In fact, certain subsets of three of the two-body marginals suffice for the characterization. We also discuss generalizations of the statement to pure states of more particles, showing that these are almost always determined among pure states by three of their $(n-2)$-body marginals. Finally, we present special families of symmetric pure four-particle states that share the same two-body marginals and are therefore undetermined. These are four-qubit Dicke states in superposition with generalized GHZ states.