1,404 research outputs found
Unbounded violations of bipartite Bell Inequalities via Operator Space theory
In this work we show that bipartite quantum states with local Hilbert space
dimension n can violate a Bell inequality by a factor of order (up
to a logarithmic factor) when observables with n possible outcomes are used. A
central tool in the analysis is a close relation between this problem and
operator space theory and, in particular, the very recent noncommutative
embedding theory. As a consequence of this result, we obtain better Hilbert
space dimension witnesses and quantum violations of Bell inequalities with
better resistance to noise
Large violation of Bell inequalities with low entanglement
In this paper we obtain violations of general bipartite Bell inequalities of
order with inputs, outputs and
-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a
random choice of signs, all the elements involved in such violations: the
coefficients of the Bell inequalities, POVMs measurements and quantum states.
Analyzing this construction we find that, even though entanglement is necessary
to obtain violation of Bell inequalities, the Entropy of entanglement of the
underlying state is essentially irrelevant in obtaining large violation. We
also indicate why the maximally entangled state is a rather poor candidate in
producing large violations with arbitrary coefficients. However, we also show
that for Bell inequalities with positive coefficients (in particular, games)
the maximally entangled state achieves the largest violation up to a
logarithmic factor.Comment: Reference [16] added. Some typos correcte
BMO spaces associated with semigroups of operators
We study BMO spaces associated with semigroup of operators and apply the
results to boundedness of Fourier multipliers. We prove a universal
interpolation theorem for BMO spaces and prove the boundedness of a class of
Fourier multipliers on noncommutative Lp spaces for all 1 < p < \infty, with
optimal constants in p.Comment: Math An
Hypercontractivity on the -Araki-Woods algebras
Extending a work of Carlen and Lieb, Biane has obtained the optimal
hypercontractivity of the -Ornstein-Uhlenbeck semigroup on the
-deformation of the free group algebra. In this note, we look for an
extension of this result to the type III situation, that is for the
-Araki-Woods algebras. We show that hypercontractivity from to
can occur if and only if the generator of the deformation is bounded.Comment: 17 page
Connes' embedding problem and Tsirelson's problem
We show that Tsirelson's problem concerning the set of quantum correlations
and Connes' embedding problem on finite approximations in von Neumann algebras
(known to be equivalent to Kirchberg's QWEP conjecture) are essentially
equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite
quantum correlations generated between tensor product separated systems is the
same as the set of correlations between commuting C*-algebras. Connes'
embedding problem asks whether any separable II factor is a subfactor of
the ultrapower of the hyperfinite II factor. We show that an affirmative
answer to Connes' question implies a positive answer to Tsirelson's.
Conversely, a positve answer to a matrix valued version of Tsirelson's problem
implies a positive one to Connes' problem
Resonance energy transfer: The unified theory revisited
Resonanceenergy transfer (RET) is the principal mechanism for the intermolecular or intramolecular redistribution of electronic energy following molecular excitation. In terms of fundamental quantum interactions, the process is properly described in terms of a virtual photon transit between the pre-excited donor and a lower energy (usually ground-state) acceptor. The detailed quantum amplitude for RET is calculated by molecular quantum electrodynamical techniques with the observable, the transfer rate, derived via application of the Fermi golden rule. In the treatment reported here, recently devised state-sequence techniques and a novel calculational protocol is applied to RET and shown to circumvent problems associated with the usual method. The second-rank tensor describing virtual photon behavior evolves from a Green’s function solution to the Helmholtz equation, and special functions are employed to realize the coupling tensor. The method is used to derive a new result for energy transfer systems sensitive to both magnetic- and electric-dipole transitions. The ensuing result is compared to that of pure electric-dipole–electric-dipole coupling and is analyzed with regard to acceptable transfer separations. Systems are proposed where the electric-dipole–magnetic-dipole term is the leading contribution to the overall rate
Joint system quantum descriptions arising from local quantumness
Bipartite correlations generated by non-signalling physical systems that
admit a finite-dimensional local quantum description cannot exceed the quantum
limits, i.e., they can always be interpreted as distant measurements of a
bipartite quantum state. Here we consider the effect of dropping the assumption
of finite dimensionality. Remarkably, we find that the same result holds
provided that we relax the tensor structure of space-like separated
measurements to mere commutativity. We argue why an extension of this result to
tensor representations seems unlikely
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