A mixed quantum mechanical problem

Roberto Laura, Mario Castagnino

A formalism for minimal irreversible quantum mechanics is extended from pure states to mixed states. In the latter case the problem of their diagonal singularity is explained and solved. In addition to the pure and mixed states of the usual approach, more general states are obtained. The Friedrichs model is studied. Decoherence is found and decoherence characteristic times are computed.

Francis J. Narcowich

L. L. J. Vick

Hao Chen

A mixed state may be represented in many different ways as a mixture of pure states ρ=∑pi∣ψi⟩⟨ψi∣. The mixing problem in quantum mechanics asks the characterization of the probability distribution (pi) and the mixed states (ρi) such that ρ=∑piρi for any given mixed state ρ. Some constraints based on eigenvalues of the mixed states are established in uni-party case [see Nielsen, Phys. Rev. A. 63, 052308 (2000), 63, 022144 (2000), Nielsern and Vidal Quantum Inf. Comput. 1 76 (2001)]. We develop some new invariant sets for bipartite mixed states under local unitary operations, which are independent of eigenvalues, and prove some strong constraints based on these invariant sets for the mixing problem in bipartite case. This exhibits a remarkable difference from the uni-party case.

Thomas Jörg, Florent Krząkała, Jorge Kurchan B +1 more

Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems for which the efficiency can be studied analytically using techniques based on the statistical mechanics of spin glasses.

Gennaro Auletta