3 research outputs found
Monogamy of Bell correlations and Tsirelson's bound
We consider three parties, A, B, and C, each performing one of two local measurements on a shared quantum state of arbitrary dimension. We characterize the trade-off between the nonlocality of the Bell correlations observed by AB and of those observed by AC. This generalizes Tsirelson's bound on the quantum value of the CHSH inequality, the latter being recovered when C is completely uncorrelated with AB. We also discuss the trade-off between Bell violations and local expectation values of observables that anticommute with the ones used in the Bell test
A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
We are interested in the problem of characterizing the correlations that
arise when performing local measurements on separate quantum systems. In a
previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite
hierarchy of conditions necessarily satisfied by any set of quantum
correlations. Each of these conditions could be tested using semidefinite
programming. We present here new results concerning this hierarchy. We prove in
particular that it is complete, in the sense that any set of correlations
satisfying every condition in the hierarchy has a quantum representation in
terms of commuting measurements. Although our tests are conceived to rule out
non-quantum correlations, and can in principle certify that a set of
correlations is quantum only in the asymptotic limit where all tests are
satisfied, we show that in some cases it is possible to conclude that a given
set of correlations is quantum after performing only a finite number of tests.
We provide a criterion to detect when such a situation arises, and we explain
how to reconstruct the quantum states and measurement operators reproducing the
given correlations. Finally, we present several applications of our approach.
We use it in particular to bound the quantum violation of various Bell
inequalities.Comment: 33 pages, 2 figure