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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Mechanics

MP 3.1: Vortrag

Montag, 30. März 2020, 17:15–17:35, H-HS VII

Systematic construction of k-uniform states — •Zahra Raissi¹, Adam Teixid¹, Christian Gogolin^1,2,3, and Antonio Acin^1,4 for the A4 collaboration — ¹ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain — ²Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany — ³Xanadu, Toronto, M5V 1X6, Canada — ⁴ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain

Absolutely maximally entangled (AME) states are pure quantum states of n-partite systems of local dimension q with the property that all reduced states (marginals) of at most half the system size are maximally mixed. AME states are special cases of the class of so-called k-uniform states for k =⌊ n/2⌋. These states are useful for some protocols like multipartite teleportation, have connections with combinatorial designs, and quantum error correcting codes (QECC). They are also relevant for the construction of holographic codes.

To our knowledge, the only known systematic construction of these states is based on a class of classical error correction codes known as Maximum Distance Separable (MDS) code. In this work, we present a systematic method to construct other examples of k-uniform states. We also show that the states derived through our construction are not Local Unitary (LU) equivalent to any k-uniform state constructed from minimum-distance separable codes.