One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. It is natural to ask if such states exist in a given quantum system and how do they look like. During my talk, I will briefly explain why such states are important. Then, I will introduce some relevant notions, such as diagonal H-symmetries, and move to the main technical result which states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. The rest of the talk will be devoted to the applications of the main result with its corollaries and examples of designing critical states with large local unitary symmetry. In particular, I will explain that critical states with large local symmetries can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. I will also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries.
Zoom meeting details
Topic: Quantum Information and Quantum Computing Working Group
Time: Thursday, September 30, 2021, 15:15 Warsaw (CET)
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