Mixed Quantum States and the Density Operator

Gilbert Reinisch

Gilbert Reinisch

Alice Flarend, Robert Hilborn

Abstract Probability density operators are a generalization of the concept of quantum states and provide a framework for describing mixed quantum states, which are weighted mixtures of pure quantum states. These mixed states are essential in describing how a quantum system interacts with its environment, a critical issue in quantum computing and quantum information science. The chapter also covers the time dependence of density operators and their relationship to quantum measurements.

Vasily Evgenevich Tarasov

Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of $4^{n}$-dimensional operator Hilbert space. Unitary quantum gates and nonunitary quantum operations for n-qubit system are considered as generalized quantum gates acting on mixed state. In this paper we study universality for quantum computations by quantum operations on mixed states.

Maurice A. de Gosson