A Decision Theory in Non-commutative Domain

In the later part of my professional life in the Indian Statistical Institute (I.S.I.), when I left Delhi to take up the position of the Director of I.S.I. in Kolkata, Aloke was my pillar of support, my person-to-go-to in any crisis; his was the shoulder to cry on. Those were, in many ways, difficult times for me and often I reflect and wonder how those times would have been without Aloke. In fact, from the mid-nineties, Aloke, in his extremely pleasant, shy and humble way, slowly but surely entered into a very close friendship in my life, which I will cherish forever. My frequent travels to Delhi, well after my retirement from I.S.I., would bring me to I.S.I., Delhi and to me that meant spending time with Aloke, long discussions inevitably ending with a very pleasant lunch with him in the Chinese restaurant, opposite the gate of I.S.I. All these will remain only memories now and my next visit to Delhi (delayed by Covid-19) will be empty, "Aloke-heen" (in Bengali), and will make me miss him all the more. The following article, a brief introduction (by a non-expert) to the decision theory in a non-commutative (quantum-) background, is my humble tribute to Aloke and to his friendship for me.