Hi! My name is Suhail Ahmad Rather. I am a theoretical physicist with research interests in quantum information, many-body physics, quantum chaos, mathematical physics, and dynamical systems. I did Ph.D. under the supervision of Prof. Arul Lakshminarayan in the Department of Physics at the Indian Institute of Technonlogy Madras. Presently I am working as a postdoctoral researcher at MPIPKS Dresden, Germany, in the group of Dr. Pieter Claeys.

## Highlights of recent works:

New work on arXiv: "On classifying absolutely maximally entangled states and the infinitude of inequivalent quantum solutions to the problem of 36 officers of Euler". In this work, we examined the equivalence among four-party absolutely maximally entangled (AME) states based on local unitary (LU) equivalence. Quite surprisingly we proved that there is only one unique AME of four qutrits (three-level quantum systems) up to multiplication by single-qutrit unitary gates. However for local dimension greater than 3 (i.e., ququads and above) we show that there are uncountably infinite AME states. Such inequivalent AME states in local dimension six provide quantum solutions to the thirty-six officers problem of Euler.

New work on arXiv: "Dual unitaries as maximizers of the distance to local product gates" This work was an exciting collaboration with Shrigyan Brahmachari and Rohan Narayan Rajmohan who were undergraduate project students in our group.

Highlights of previous works:

Popular write ups on our recent work Phys. Rev. Lett.128.080507:

Article in the Quanta Magazine by Dan Garisto.

Physics Focus story by well known science writer and author Philip Ball.

Article in The Hindu newspaper by Shubashree Desikan.

Our work Phys. Rev. Lett. 128, 080507 was published as Editors suggestion. In this work, we positively settled a long standing open problem regarding the existence of absolutely maximally entangled states of four six level systems. We give an explicit construction of such a state in terms of an entangled orthogonal quantum Latin squares (OQLS) of size six. It's classical counterpart, an orthogonal Latin squares (OLS) of size six, does not exist a fact known in combinatorics with interesting history which dates back to Euler (1779).

Four dice in the absolutely maximally entangled state of four six level systems. Any pair of dice is unbiased, although their random outcomes determine the state of other two. This is not possible if the four dice are replaced by four coins (qubits).

Dynamics in the Weyl chamber: Convergence to dual-unitaries in the two-qubit case.

(Journal ref: Phys. Rev. Lett. 125, 070501)

Role of the entangling power in constructing quantum ergodic hierarchy in dual-unitary circuits

(Journal ref: Phys. Rev. Research 3 043034)

In our work recent arXiv:2104.05122 , we solved positively a well known open problem regarding the existence of AME(4,6) (Absolutely Maximally Entangled state of four subsystems each having six levels). We showed that although classical solution does not exist due to the non-existence of orthogonal Latin squares (OLS) of size six but the quantum solution; an entangled OLS of size six , exists.

Entangled OLS of order six corresponding to AME(4,6) . The classical solution if it exists would just contain only the one card (shown in larger font) in each cell. (Image credit: Grzegorz Rajchel-Mieldzioć)