Assume Alice and Bob share some bipartite $d$-dimensional quantum state. A
well-known result in quantum mechanics says that by performing two-outcome
measurements, Alice and Bob can produce correlations that cannot be obtained
locally, i.e., with shared randomness alone. We show that by using only two
bits of communication, Alice and Bob can classically simulate any such
correlations. All previous protocols for exact simulation required the
communication to grow to infinity with the dimension $d$. Our protocol and
analysis are based on a power series method, resembling Krivine's bound on
Grothendieck's constant, and on the computation of volumes of spherical
tetrahedra.Comment: 19 pages, 3 figures, preliminary version in IEEE FOCS 2007; to appear
  in SICOM

Regev, Oded

Toner, Ben

SIAM Journal on Computing

English

arXiv

Assume Alice and Bob share some bipartite d-dimensional quantum state. A well-known result in quantum mechanics says that by performing two-outcome measurements, Alice and Bob can produce correlations that cannot be obtained locally, i.e., with shared randomness alone. We show that by using only two bits of communication, Alice and Bob can classically simulate any such correlations. All previous protocols for exact simulation required the communication to grow to infinity with the dimension d. Our protocol and analysis are based on a power series method, resembling Krivine's bound on Grothendieck's constant, and on the computation of volumes of spherical tetrahedra

Caltech Authors - Main

Simulating Quantum Correlations with Finite Communication

Regev, O

Toner, B

University of Melbourne Institutional Repository

Simulating quantum correlations with finite communication

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https://authors.library.caltech.edu/18727/1/Regev2009p10151Siam_J_Comput.pdf

Simulating Quantum Correlations with Finite Communication

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Caltech Authors - Main

Caltech Authors - Main

University of Melbourne Institutional Repository