Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistically Perfect Cloning of Two Pure States: A Geometric
  Approach   We solve the long-standing problem of making n perfect clones from m copies
of one of two known pure states with minimum failure probability in the general
case where the known states have arbitrary a priori probabilities. The solution
emerges from a geometric formulation of the problem. This formulation also
reveals a deeper connection between cloning and state discrimination. The
convergence of cloning to state discrimination as the number of clones goes to
infinity exhibits a phenomenon analogous to a second order symmetry breaking
phase transition.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph