A Galois Theory of Quantum Error Correcting Codes

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• We prepare the two silver atoms in the state
• The Kings men measure the state of one atom, so
  the state will collapse to

• We need to device a measurement of both atoms
  such that the result specifies a function f from
  bases to measurement values
• If the King reveals the basis a, then f(a)
  should give the value b which has been measured
  by the Kings men.

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So suppose we have a function fx,y,z-gt0,1 th
en we can define an entangled state by These
state will define our measurements of the states.
Did you notice that we average over the three
bases?
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• A (v,k,l) design over a finite set X of v points
  is a
• a family of k-subsets of X, called blocks
• such that each pair of points is contained in l
  blocks
• Any point of X lies in r (v-1) l / (k-1)
  blocks
• The design has vr/k blocks

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An (n2,n,1) design is called an affine plane of
order n. It has n2 points and n2n lines
(blocks). Each line consists of n
points. Example Affine plane of order 2
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An affine plane of order n has n1 parallel
classes Lk of lines (two lines are parallel if
the do not intersect or if they are the
same) We assume that L0 contains lines lx
(x,1),(x,2),...,(x,n)
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