Operator space theory: a natural framework for bell inequalities

TY - JOUR

T1 - Operator space theory

T2 - a natural framework for bell inequalities

AU - Junge, M.

AU - Palazuelos, C.

AU - Perez-Garcia, D.

AU - Villanueva, I.

AU - Wolf, Michael Marc

PY - 2010/4/29

Y1 - 2010/4/29

N2 - In this Letter we show that the field of operator space theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular, regarding the scaling of their violation within quantum mechanics. We illustrate the power of this connection by showing that bipartite quantum states with local, Hilbert space dimension n can violate a Bell inequality by a factor of order √n/(log2n) when observables with n possible outcomes are used. Applications to resistance to noise, Hilbert space dimension estimates, and communication complexity are given.

AB - In this Letter we show that the field of operator space theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular, regarding the scaling of their violation within quantum mechanics. We illustrate the power of this connection by showing that bipartite quantum states with local, Hilbert space dimension n can violate a Bell inequality by a factor of order √n/(log2n) when observables with n possible outcomes are used. Applications to resistance to noise, Hilbert space dimension estimates, and communication complexity are given.

U2 - 10.1103/PhysRevLett.104.170405

DO - 10.1103/PhysRevLett.104.170405

M3 - Journal article

SN - 0031-9007

VL - 104

SP - 170405

JO - Physical Review Letters

JF - Physical Review Letters

IS - 17

ER -