Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session M35: General Quantum Information I
8:00 AM–11:00 AM,
Wednesday, March 16, 2022
Room: McCormick Place W-193B
Sponsoring Unit: DQI
Chair: Manish Kumar Singh, University of Chicago
Abstract: M35.00001 : Hierarchical graph states of k-uniform and absolutely maximally entangled states
8:00 AM–8:12 AM
The k-uniform states are a particular type of highly entangled states, all of their reductions to k parties are maximally-mixed. A special case of this set are AME states that are maximally entangled along any splitting of parties into two groups. Moreover, the graph states are another set of well-entangled quantum states defined based on a graph, are also a class of stabilizer states.
We present a hierarchical procedure that leads us to study the geometric structure of k-uniform and AME states in the graph states representation. First, we introduce the most generalized method of constructing k-uniform and AME states from classical-error-correcting codes. Next, we introduce hierarchical graph states that construct the highly entangled states by iterating a certain geometric structure in graph state representation. We also show at each level of iteration the states that are all k-uniform cannot be converted into each other by SLOCC (stochastic local operations and classical communication).
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