ELFT HÍRADÓ

[Balog Janos <balog.janos AT wigner.mta.hu>]

MTA Wigner FK RMI Elméleti Osztály Szemináriuma
Tisztelettel meghívjuk


                        Robert Zeier
                (Technische Universität München)

  "Controllability and symmetries of coupled quantum systems"


             címmel tartandó szemináriumára.

Kivonat:
We study finite-dimensional quantum systems and their symmetries using 
representation-theoretic methods in the context of Lie algebras and Lie 
groups. The convenience of this approch is exemplified in two particular 
cases. First, we ask what one can do with a given coupled quantum system 
whose time evolution is to a certain degree externally controllable. We 
present a technique based on analyzing symmetries which decides if a 
controlled quantum system can simulate a given effective Hamiltonian. 
Moreover, our technique can compare the respective computational power 
of two controlled quantum systems. We emphasize that our approach 
improves on the conventional approach of computing Lie-closures of 
generators and harnesses the symmetries of the quantum system in order 
to reduce Lie-algebraic computations to effective linear-algebra ones. 
On a mathematical level, this question is related to the study of how 
tensor products of representations decompose when restricted from a 
compact Lie algebra to one of its subalgebras. Second, coupled quantum 
systems exhibit an intricate structure not explained by properties of 
their subsystems alone. We study the plethora of emerging symmetries 
that are invariant under local operations, i.e., operations which do not 
lead to interactions between the subsystems. We enumerate these 
symmetries by computing Hilbert series and also explore connections to 
so-called Kronecker coefficients. We particularly focus on the case of 
three-qubit mixed states. Our approach provides a new foundation for 
better understanding non-local quantum states. In general, our point of 
view highlights the utility of algebraic and representation-theoretic 
tools for analyzing quantum systems.


Helye: MTA Wigner FK RMI III.ép. Tanácsterem
Ideje: 2017 június 16  péntek du. 14:00 óra



Szívesen látunk minden érdeklődőt.

                                            Balog János