Entanglement distance for arbitrary $M$-qudit hybrid systems

• URL: http://arxiv.org/abs/2003.05771v1
• Date: Wed, 11 Mar 2020 15:16:36 GMT
• Title: Entanglement distance for arbitrary $M$-qudit hybrid systems
• Authors: Denise Cocchiarella (1), Stefano Scali (2,3), Salvatore Ribisi (4), Bianca Nardi (1), Ghofrane Bel-Hadj-Aissa (1,5), Roberto Franzosi (5) ((1) DSFTA, University of Siena, Italy, (2) Department of Physics, University of Cambridge, United Kingdom, (3) Department of Physics and Astronomy, University of Exeter, United Kingdom, (4) Centre de Physique Th\'eorique, Aix-Marseille University, France, (5) QSTAR & CNR - Istituto Nazionale di Ottica, Firenze, Italy)
• Abstract summary: We propose a measure of entanglement which can be computed for pure and mixed states of a $M$-qudit hybrid system. We quantify the robustness of entanglement of a state through the eigenvalues analysis of the metric tensor associated with it.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications. However, to exploit the advantages of such states, we need a thorough characterisation of their entanglement. Here, we propose a measure of entanglement which can be computed either for pure and mixed states of a $M$-qudit hybrid system. The entanglement measure is based on a distance deriving from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and has an explicit computable expression that we derive. In the specific case of $M$-qubit systems, the measure assumes the physical interpretation of an obstacle to the minimum distance between infinitesimally close states. Finally, we quantify the robustness of entanglement of a state through the eigenvalues analysis of the metric tensor associated with it.

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