Quantum evolution of words

Jȩdrzej Stempin, Jan Wójcik, Gabriela Banaszak +4 more

We introduce a quantum analogue of a classical synchronizing automaton. In classical case the state of a system evolves according to a set of rules forming an alphabet, and sequences of these rules, called words, govern its evolution. Certain special words, known as synchronizing words, drive the automaton into a predetermined state regardless of its initial configuration. Although such an apparently irreversible process seems incompatible with the unitarity of quantum mechanics, we present a resetting protocol based on quantum synchronizing words by incorporating auxiliary qubits whose states encode the rules of the automaton's alphabet. These qubits interact with the quantum automaton, whose state is encoded in a qudit, via a global unitary operation. When the qubit register is initially prepared in a state corresponding to a synchronizing word, the automaton evolves into a predetermined pure state independent of its initial state, while the qubit register is transformed into a complex, often entangled, state that encodes information about the automaton's original configuration. The resulting entanglement depends on both the rule set and the automaton's initial state, and we show how specific entangled states can be generated within this framework.

Włodzimierz Sedlak

Jonathan Bate

V. I. Gerasimenko

In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In addition, an approach to the description of the evolution of states by means of the state of a typical particle of a quantum system of many particles is discussed or in other words, the foundations of describing the evolution of states by kinetic equations are considered.

R. D. Hazeltine

We introduce the key ideas and mathematical tools central to modern discussions of collapse. We assume knowledge of basic quantum mechanics -- the Schrödinger evolution of states in Hilbert space, the Born probability rule, the Dirac formalism, and so on -- while explicating such ideas as projectors, density operators, Bell inequalities, entanglement and the Lindblad equation. In other words this work is a \emph{primer} in the simplest sense of that word: without taking a stand on the major questions, it is intended to make an enormous and growing body of research more accessible.