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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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
this?
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
The Einstein-Podolsky-Rosen paradox (1935)
EPR’s assumptions:
“Every element of the physical reality must have a counterpart in the physical theory”.
Accurate prediction ofa physical quantity → element of reality associated to it.
No action at a distance
They considered a nonfactorizable state of the form:
Steve Jones, PIAF, 2 February '08
Alice
Bob
XA, PA
XB, PB
Quantum Mechanics predicts, for certain entangled states, xA = xB and pA = - pB; by measuring at A one can predict with certainty either xBor pB .
Therefore, elements of reality must exist for both xBand pB , but QM doesn’t predict these simultaneously.
Steve Jones, PIAF, 2 February '08
“By the interaction the two representatives (or -functions) have become entangled.”
“What constitutes the entanglement is that is not a product of a function for x and a function for y.”
Steve Jones, PIAF, 2 February '08
Schrodinger’s 1935 response to EPR
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
Separable: A local hidden state (LHS) model for both parties
Non-steerable: A local hidden state (LHS) model for one party
Bell local: A local hidden variable (LHV) model for both parties
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
That is, do they violate the assumption of a local hidden state model for Bob?
Any sufficient criterion for experimental steering will be called a steering criterion.
Steve Jones, PIAF, 2 February '08
Any sufficient criterion for state steerability will be called a steerability witness.
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
Lemma: A bipartite density matrix on is steerable if and only if there exists a Hermitian operator such that
and for all non-steerable density matrices .
However, the measurements required to determine do not necessarily violate a LHS model.
Compare with Bell-nonlocality witnesses vs Bell inequalities
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
→ harder for her to steer to a given ensemble.
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08
Steve Jones, PIAF, 2 February '08