Francesco Buscemi (Nagoya University), Institute for Quantum Computing (IQC)
Abstract
Title: - All entangled quantum states are nonlocal: equivalence between locality and separability in quantum theory
In this talk I will show how, by slightly modifying the rules of
nonlocal games, one can prove that all entangled states violate local
realism.
As it is well known, Bell inequalities, which are used to test the
violation of local realism, can be equivalently reformulated in terms
of nonlocal games (namely, cooperative games with incomplete
information) played between one referee and two (or more) players,
these latter being separated so to make any form of communication
between them impossible during the game. Quantum nonlocality is that
property of quantum states that allows players sharing them to win
nonlocal games more frequently than the assumption of local realism
would imply.
However, as Werner proved in 1989, not all quantum states enable such
a violation of local realism. In particular, Werner showed the
existence of quantum states that cannot be created locally (the
so-called "entangled" states) and, yet, do not allow any violation of
local realism in nonlocal games. This fact has been since then
considered an unsatisfactory gap in the theory, attracting a
considerable amount of attentions in the literature.
In this talk I will present a simple proof of the fact that all
entangled states indeed violate local realism. This will be done by
considering a new larger class of nonlocal games, which I call
"semiquantum," differing from the old ones merely in that the referee
can now communicate with the players through quantum channels, rather
than being restricted to use classical ones, as it was tacitly assumed
before. I will then prove that one quantum state always provides
better payoffs than another quantum state, in semiquantum nonlocal
games, if and only if the latter can be obtained from the former, by
local operations and shared randomness (LOSR). The main claim will
then follow as a corollary.
The new approach not only provides a clear theoretical picture of the
relation between locality and separability, but also suggests, thanks
to its simplicity, new experimental tests able in principle to verify
the violation of local realism in situations where previous
experiments would fail.
Based on http://arxiv.org/abs/1106.6095