Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projecting onto Qubit Irreps of Young Diagrams   Let K be the diagonal subgroup of U(2)^{(x)n}. We may view the one-qubit
state-space H_1 as a standard representation of U(2) and the n-qubit state
space H_n=(H_1)^{(x) n} as the n-fold tensor product of standard
representations. Representation theory then decomposes H_n into irreducible
subrepresentations of K parametrized by combinatorial objects known as Young
diagrams. We argue that n-1 classically controlled measurement circuits, each a
Fredkin-gate interferometer, may be used to form a projection operator onto a
random Young diagram irrep within H_n. For H_2, the two irreps happen to be
orthogonal and correspond to the symmetric and wedge product. The latter is
spanned by ket{Psi^-}, and the standard two-qubit swap interferometer requiring
a single Fredkin gate suffices in this case. In the n-qubit case, it is
possible to extract many copies of ket{Psi^-}. Thus applying this process using
nondestructive Fredkin interferometers allows for the creation of entangled
bits (e-bits) using fully mixed states and von Neumann measurements.

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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin