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         Steering witnesses and criteria
         for the (non-)existence of local
           hidden state (LHS) models
                    Eric Cavalcanti, Steve Jones, Howard Wiseman

                    Centre for Quantum Dynamics, Griffith University

                                     Steve Jones, PIAF, 2 February ‘08
Interesting questions that I don’t plan to
address…
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              Steve Jones, PIAF, 2 February '08   1
Outline (or what I actually will talk about)

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              Steve Jones, PIAF, 2 February '08   2
The Einstein-Podolsky-Rosen paradox (1935)

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            ci ui  i   d j v j  j
               i                      j
               Steve Jones, PIAF, 2 February '08   3
The Einstein-Podolsky-Rosen paradox (1935)

       Alice                                       Bob

       XA, PA                                       XB, PB




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                Steve Jones, PIAF, 2 February '08            4
Schrodinger’s 1935 response to EPR
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           Steve Jones, PIAF, 2 February '08       5
Schrodinger’s 1935 response to EPR
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           Steve Jones, PIAF, 2 February '08   6
What about mixed states?
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          Steve Jones, PIAF, 2 February '08   7
Mathematical definitions

P(A, B a,b,c)   P( c) PQ (A a,c,  ) PQ (B b,c,  )
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P(A, B a,b,c)   P( c) P(A a,c,  ) PQ (B b,c,  )
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P(A, B a,b,c)   P( c) P(A a,c,  ) P(B b,c,  )
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                 Steve Jones, PIAF, 2 February '08   8
Why experimental steering criteria?
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           Steve Jones, PIAF, 2 February '08   9
Two types of problems

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         Steve Jones, PIAF, 2 February '08   10
Two types of problems

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         Steve Jones, PIAF, 2 February '08   11
Review: (linear) Entanglement witnesses




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            Steve Jones, PIAF, 2 February '08   12
Steerability Witnesses
                                              H  H 
                                                         ˆ
                                                         S
                               ˆ
                          Tr  S    0
                              
        ˆ
   Tr  S   0                                               
       

                                                                  ˆ
                                                             Tr  S 
                                                                 




                   Steve Jones, PIAF, 2 February '08                 13
Witnesses and experimental criteria


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           Steve Jones, PIAF, 2 February '08   14
Experimental steering criteria

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        P(A, B a,b,c)   P( c) P(A a,c,  ) PQ (B b,c,  )
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                      Steve Jones, PIAF, 2 February '08        15
Loop-holes
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         Steve Jones, PIAF, 2 February '08   16
Loop-holes
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         Steve Jones, PIAF, 2 February '08   17
Loop-holes
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            Steve Jones, PIAF, 2 February '08   18
    Steering criteria example
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                                               ˆ
                                               I
           W                  (1   )
                                               4
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                   1 n ˆ ˆ
                      Ai Bi  cn
                   n i 1
    •                                            1 / 2  0.707

    •                      1 / 3  0.577

               Steve Jones, PIAF, 2 February '08                   19
Summary and open problems
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         Steve Jones, PIAF, 2 February '08   20

								
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