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QI: Fachverband Quanteninformation

QI 1: Quantum Foundations

QI 1.4: Vortrag

Montag, 18. März 2024, 10:30–10:45, HFT-FT 101

State reachability in isolated systems with 2-body Hamiltonians — •Konrad Szymanski — Universität Siegen, Siegen, Germany

In the most basic physical systems, the dynamics is governed by time-independent 2-body interactions. A natural question arises: is the entire set of states explored if an arbitrary classical initial state and interaction pattern can be chosen? Different definitions are possible: for qubits, the pure product states are evolved with Hamiltonians composed by combinations of length-2 and 1 Pauli strings.

Only trivial conserved quantities exist in the general case, which limits the available approaches to investigate this reachability problem. Nevertheless, we show that unreachable states exist for a sufficiently complex model system. However, the problem for the most general models remains unsolved, and we present related open questions.

Keywords: autonomous dynamics; state reachability; polynomial theory; semidefinite programming; isolated systems