I2-DMSO Promoted Deaminative Coupling Reactions of Glycine Esters: Access to 5-(Methylthio)pyridazin-3(2H)-ones.

An unprecedented, one-step strategy for the synthesis of 5-(methylthio)pyridazin-3(2H)-one derivatives has been developed through iodine triggered deaminative coupling of glycine esters with methyl ketones and hydrazine hydrate in DMSO. These transformations in the absence of hydrazine helped to generate different 3-methylthio-4-oxo-enoates in good yields. Notably, DMSO played multiple roles such as oxidant, methylthiolating reagent, and solvent.

Thirty-six Entangled Officers of Euler: Quantum Solution to a Classically Impossible Problem.

The negative solution to the famous problem of 36 officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers are entangled, and construct orthogonal quantum Latin squares of this size. As a consequence, we find an example of the long-elusive Absolutely Maximally Entangled state AME(4,6) of four subsystems with six levels each, equivalently a 2-unitary matrix of size 36, which maximizes the entangling power among all bipartite unitary gates of this dimension, or a perfect tensor with four indices, each running from one to six. This special state deserves the appellation golden AME state, as the golden ratio appears prominently in its elements. This result allows us to construct a pure nonadditive quhex quantum error detection code ((3,6,2))_{6}, which saturates the Singleton bound and allows one to encode a six-level state into a triplet of such states.

Creating Ensembles of Dual Unitary and Maximally Entangling Quantum Evolutions.

Maximally entangled bipartite unitary operators or gates find various applications from quantum information to many-body physics wherein they are building blocks of minimal models of quantum chaos. In the latter case, they are referred to as "dual unitaries." Dual unitary operators that can create the maximum average entanglement when acting on product states have to satisfy additional constraints. These have been called "2-unitaries" and are examples of perfect tensors that can be used to construct absolutely maximally entangled states of four parties. Hitherto, no systematic method exists in any local dimension, which results in the formation of such special classes of unitary operators. We outline an iterative protocol, a nonlinear map on the space of unitary operators, that creates ensembles whose members are arbitrarily close to being dual unitaries. For qutrits and ququads we find that a slightly modified protocol yields a plethora of 2-unitaries.