Noether’s theorem for dissipative quantum dynamical semi-groups

Some Quantum Dynamical Semi-groups with Quantum Stochastic Dilation

We consider the GNS Hilbert space H of a uniformly hyper-finite C∗algebra and study a class of unbounded Lindbladian arises from commutators. Exploring the local structure of UHF algebra, we have shown that the associated Hudson-Parthasarathy type quantum stochastic differential equation admits a unitary solution. The vacuum expectation of homomorphic cocycle, implemented by the Hudson-Parthasa...

Dissipative quantum Church-Turing theorem.

We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Chu...

Dynamical Quantum Groups - the Super Story

We review recent results in the study of quantum groups in the super setting. In particular, we provide an overview of results about solutions of the Yang-Baxter equations in the super setting and begin to develop the super analog of the theory of dynamical quantum groups.

Quantum Groups and Von Neumann Theorem

We discuss the q deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the q-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. PACS 02.20.+b; 03.65.Fd; 11.30.Qc;

Dissipative Dynamical Systems