Scientific Results

Entanglement distance for arbitrary M-qudit hybrid systems

Year: 2020

Authors: Cocchiarella D., Scali S., Ribisi S., Nardi B., Bel-Hadj-Aissa G., Franzosi R.

Autors Affiliation: DSFTA, University of Siena, Via Roma 56, 53100 Siena, Italy
Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom 3Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom 4Centre de Physique Th ́eorique, Aix-Marseille University,
Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France
QSTAR & CNR – Istituto Nazionale di Ottica, Largo Enrico Fermi 2, I-50125 Firenze, Italy

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.

Journal/Review: PHYSICAL REVIEW A

Volume: 101      Pages from: 042129-1  to: 042129-9

KeyWords: Entanglement measure.
DOI: 10.1103/PhysRevA.101.042129