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: Univ Siena, DSFTA, Via Roma 56, I-53100 Siena, Italy; Univ Cambridge, Dept Phys, Cambridge CB3 0HE, England; Univ Exeter, Dept Phys & Astron, Exeter EX4 4QL, Devon, England; Aix Marseille Univ, Ctr Phys Theor, Campus Luminy,Case 907, F-13288 Marseille 09, France; QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; CNR, Ist Nazl Ott, Largo Enrico Fermi 2, I-50125 Florence, 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 (4)      Pages from: 42129-1  to: 42129-9

More Information: R.F. acknowledges support by the QuantERA ERA-NET Co-fund 731473 (Project Q-CLOCKS). S.S. is supported by the Engineering and Physical Sciences Research Council (EPSRC) through a doctoral training grant.
KeyWords: Quantum; Purification; Geometry; State
DOI: 10.1103/PhysRevA.101.042129

Citations: 7
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