Linear maps of matrices describing evolution of density matrices for a
quantum system initially entangled with another are identified and found to be
not always completely positive. They can even map a positive matrix to a matrix
that is not positive, unless we restrict the domain on which the map acts.
Nevertheless, their form is similar to that of completely positive maps. Only
some minus signs are inserted in the operator-sum representation. Each map is
the difference of two completely positive maps. The maps are first obtained as
maps of mean values and then as maps of basis matrices. These forms also prove
to be useful. An example for two entangled qubits is worked out in detail.
Relation to earlier work is discussed.Comment: 4 figure
Simple examples are presented of Lorentz transformations that entangle the
spins and momenta of two particles with positive mass and spin 1/2. They apply
to indistinguishable particles, produce maximal entanglement from finite
Lorentz transformations of states for finite momenta, and describe entanglement
of spins produced together with entanglement of momenta. From the entanglements
considered, no sum of entanglements is found to be unchanged.Comment: 5 Pages, 2 Figures, One new paragraph and reference adde
Lorentz transformations of spin density matrices for a particle with positive
mass and spin 1/2 are described by maps of the kind used in open quantum
dynamics. They show how the Lorentz transformations of the spin depend on the
momentum. Since the spin and momentum generally are entangled, the maps
generally are not completely positive and act in limited domains. States with
two momentum values are considered, so the maps are for the spin qubit
entangled with the qubit made from the two momentum values, and results from
the open quantum dynamics of two coupled qubits can be applied. Inverse maps
are used to show that every Lorentz transformation completely removes the spin
polarization, and so completely removes the information, from a number of spin
density matrices. The size of the spin polarization that is removed is
calculated for particular cases.Comment: 7 Pages, 3 Figure
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