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SUMMARY:Different permutations are almost orthogonal - Aram Harrow (Univer
 sity of Washington)
DTSTART:20120713T110000Z
DTEND:20120713T120000Z
UID:TALK38974@talks.cam.ac.uk
CONTACT:Richard Jozsa
DESCRIPTION:Consider the n! different unitaries that permute n d-dimension
 al quantum systems. If d>=n\, then these are linearly independent. In this
  talk\, I'll explain a sense in which they are approximately orthogonal\ni
 f d >> n^2. This simple fact turns out to make life much easier when worki
 ng with multipartite quantum states that are invariant under collective un
 itary rotation. After describing the basic idea\, I'll discuss some subset
  of the following five applications:\n\n1. There is no efficient product t
 est (in the sense of my previous work with Ashley Montanaro) that uses onl
 y LOCC measurements between the different copies of the state to be tested
 .\n\n2. Random maximally entangled states have similar moments to fully ra
 ndom states.\n\n3. Random quantum circuits on n qubits with poly(n) gates 
 are approximate poly(n)-designs. (Joint work with Fernando Brandao and Mic
 hal Horodecki).\n\n4. An alternate proof of the Hastings result that rando
 m unitaries give quantum expanders.\n\n5. The N-party data-hiding scheme o
 f Eggeling and Werner can be achieved with only poly(N) local dimension.
LOCATION:MR14\, Centre for Mathematical Sciences
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