Electromagnetic waves of a given wave-vector can be in one of
two independent modes or ``polarizations.'' For an electromagnetic
wave propagating along the 
direction in free space, Maxwell's
equations show that the electric field vector associated with this
wave must point in the plane perpendicular to the direction of
propagation (
, in this case). If, as the wave passes, the
electric field oscillates up and down along the x direction, the
wave is considered x-polarized. If the electric field oscillates
along the y direction, the wave is considered y-polarized.
Superposing waves of these two types of polarization can result in a
right circularly polarized wave r, where the electric field moves in
counter-clockwise circles as the wave passes or in a left circularly
polarized wave l where the field moves in clockwise circles as the
wave passes. Note that other kinds of polarization are possible!
Filters exist which pass either only x, y, r or l polarized
waves. Table 1 summarizes the result of taking a
beams of these four polarizations and passing them through each of the
filters.
Table 1: Summary of Properties of Polarization Filters
(You may wish to refer to chapter six of French and Taylor for a more detailed discussion of polarization. Be sure also to ask your recitation instructors about it. The problem is designed to be self-contained. Everything you need to answer the questions is found either in the lecture notes or in the statement of this problem.)
We know that light is composed of photons and so the classical
observable of polarization must make up part of the description of the
quantum state of the photon. Imagine that you are given a
polarization filter of the type x indicated above and are presented
with two sources of light 
and 
which you are told produce
photons in two (possibly different) quantum states A and B.
Answer as fully as you can the following questions based on
our discussion in lecture about quantum states. For each ``Is/Are...''
question, give one of the following three responses: ``Very Likely,''
``Insufficient Information,'' ``Very Unlikely.''
Give a brief explanation of each response.
Hint: Keep in mind that since photons are descrete, when they
hit a filter, they either goes through or they do not. To us, whether
or not a photon goes through the filter is the observable ``measured''
by that filter.