Quantum Dynamics of Pure and Mixed States

William George Unruh, Robert M. Wald

It has been argued that any evolution law taking pure states to mixed states in quantum field theory necessarily gives rise to violations of either causality or energy-momentum conservation in such a way as to have unacceptable consequences for ordinary laboratory physics. We show here that this is not the case by giving a simple class of examples of Markovian evolution laws where rapid evolution from pure states to mixed states occurs for a wide class of states with appropriate properties at the ``Planck scale,'' suitable locality and causality properties hold for all states, and the deviations from ordinary dynamics (and, in particular, violations of energy-momentum conservation) are unobservably small for all states which one could expect to produce in a laboratory. In addition, we argue (via consideration of other, non-Markovian models) that conservation of energy and momentum for all states is not fundamentally incompatible with causality in dynamical models in which pure states evolve to mixed states.

D. C. Hutcgings

Deng Wen-Ji, Liu Ping, Xu Xiao +1 more

Based upon the Heisenberger's uncertainty relations for mixed states, the minimu muncertainty and squeezing effects are studies. Although all minimum uncertainty states must be pure states, the nucertainty of one dynamical variable can be squeezed in some pure states or mixed states, even if they are not minimum uncert ainty states for the pair of dynamical variables. In addition, we present the ge neral uncertainty relation of statistics, which has the similar mathmatical stru cture of Heisenberg's indeterminacy principle, but has no relation with quantum interfernce.

S. Gheorghiu-Svirschevski

We argue that usual quantum statics and the dynamical equivalence of mixed quantum states to {\it probabilistic mixtures}suffice to guarantee a linear evolution law, which necessarily complies with the no-signaling condition. Alternatively, there are nonlinear dynamical extensions that treat mixed states as {\it elementary mixtures} and evolve {\it every}pure state linearly and unitarily. But if all {\it entangled} pure states evolve linearly, then elementary mixtures cannot evolve nonlinearly without challenging quantum locality. Conversely, any such extension that is relativistically well behaved demands a nonlinear evolution [decoherence] of pure entangled states. Wherefrom follows that the linear evolution of entangled pure states provides an unequivocal signature of linear quantum dynamics.

Xiang Ying Sun