Quantum Decoherence in Reduced Dimensions

Nima Arkani-hamed A, John E. Sipe

Grzegorz Pastuszak, Andrzej Jamiołkowski

Maps of the form Phi(X) =sum_{i=1}^s A_iXA^*, where A_1, . . . ,A_s are fixed complex n by n matrices and X is any complex n by n matrix are used in quantum information theory as representations of quantum channels. This article deals with computable conditions for the existence of decoherence--free subspaces for Phi. Since the definition of decoherence-free subspace for quantum channels relies only on the matrices A1, . . . ,As, the term of common reducing unitary subspace is used instead of the original one. Among the main results of the paper, there are computable conditions for the existence of common eigenvectors. These are related to common reducing unitary subspaces of dimension one. The new results on common eigenvectors provide new effective condition for the existence of common invariant subspaces of arbitrary dimensions.

Piotr Marecki

S V Rozanov, Evgeniy O. Kiktenko

We consider the problem of approximate calculation of quantum mutual information in a bipartite quantum state where one of subsystems goes through a decoherence process (quantum channel). The approximation employs a reduced density matrix of the subsystem affected by decoherence and the initial value of mutual information before decoherence. We test the approximation on sets of randomly generated qubit-qudit mixed states for three types of qubit decoherence channels: dephasing, depolarizing, and damping. We consider how approximation accuracy is related to decoherence type, decoherence strength, and the dimension of the qudit subsystem.

Maximilian Schlosshauer

Hao Xu

A bstract We study the decoherence and thermalization of an Unruh-DeWitt detector linearly coupled to the free massless scalar field in flat spacetime with arbitrary dimensions d ≥ 2. The initial state of the detector is chosen to be a pure state consisting of a linear superposition of ground and excited states, and we calculate the time evolution of reduced density matrix of the detector. Using perturbation method, we analytically derive the transition rate of the detector (the rate of change of the diagonal elements in the density matrix) and the decoherence rate (the rate of change of the off-diagonal elements in the density matrix). We find that the results are not the same in odd and even dimensional spacetimes, but the unitarity of the qubit is preserved in both cases. The real part of the decoherence rate is related to the transition rate, while the imaginary part may contain different forms of divergence terms in different dimensions due to the temporal order product operator and the singularities of the Wightman function for quantum field theory. We derive the recurrence formula to obtain the divergence terms in each dimension and analyze the renormalization problem.