Exploring Quantum Structures: Contrasting the Typical and Atypical

Exploring Quantum Structures: Contrasting the Typical and Atypical

Seminar author:Karol Życzkowski

Event date and time:11/27/2025 04:00:pm

Event location:Seminars Room, GIQ

Event contact:

We analyze the following quantum structures: the set $\Omega_N$ of mixed quantum states of order $N$, the set of discrete quantum operations (completely positive, trace preserving maps) acting on $\Omega_N$ and the set of Lindblad operators generating continuous dynamics in $\Omega_N$. On one hand, we investigate  typical quantum states, operations and Lindblad operators. In each case their statistical properties, studied with suitable ensembles of random matrices, serve as reference points. On the other hand, we look for atypical quantum objects with extremal properties and identify some examples of highly entangled multipartite states and strongly entangling quantum gates.
Furthermore, we analyze discrete structures in the Hilbert space, including quantum $t$-designs: collections of $M$ objects, chosen in such a way that the average over them approximates the average over the measure  analyzed for all functions of degree $t$. In particular, we demonstrate a link between
projective designs (consisting of pure quantum states) with classical simplex designs, mixed states quantum designs and quantum operation designs.