3,319 research outputs found
Foundational nonuniform (co)datatypes for higher-order logic
Nonuniform (or “nested” or “heterogeneous”) datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)recusion and (co)induction principles based on a weak variant of parametricity
Quantum Thermalization With Couplings
We study the role of the system-bath coupling for the generalized canonical
thermalization [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein
et al., Phys. Rev. Lett. 96, 050403(2006)] that reduces almost all the pure
states of the "universe" [formed by a system S plus its surrounding heat bath
] to a canonical equilibrium state of S. We present an exactly solvable, but
universal model for this kinematic thermalization with an explicit
consideration about the energy shell deformation due to the interaction between
S and B. By calculating the state numbers of the "universe" and its subsystems
S and B in various deformed energy shells, it is found that, for the
overwhelming majority of the "universe" states (they are entangled at least),
the diagonal canonical typicality remains robust with respect to finite
interactions between S and B. Particularly, the kinematic decoherence is
utilized here to account for the vanishing of the off-diagonal elements of the
reduced density matrix of S. It is pointed out that the non-vanishing
off-diagonal elements due to the finiteness of bath and the stronger
system-bath interaction might offer more novelties of the quantum
thermalization.Comment: 4 pages, 2 figure
Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems
It was recently shown that the nonseparable density operators for a bipartite
system are trace norm dense if either factor space has infinite dimension. We
show here that non-local states -- i.e., states whose correlations cannot be
reproduced by any local hidden variable model -- are also dense. Our
constructions distinguish between the cases where both factor spaces are
infinite-dimensional, where we show that states violating the CHSH inequality
are dense, and the case where only one factor space is infinite-dimensional,
where we identify open neighborhoods of nonseparable states that do not violate
the CHSH inequality but show that states with a subtler form of non-locality
(often called "hidden" non-locality) remain dense.Comment: 8 pages, RevTe
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Two separated observers, by applying local operations to a supply of
not-too-impure entangled states ({\em e.g.} singlets shared through a noisy
channel), can prepare a smaller number of entangled pairs of arbitrarily high
purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully
teleport unknown quantum states from one observer to the other, thereby
achieving faithful transfrom one observer to the other, thereby achieving
faithful transmission of quantum information through a noisy channel. We give
upper and lower bounds on the yield of pure singlets ()
distillable from mixed states , showing if
\bra{\Psi^-}M\ket{\Psi^-}>\half.Comment: 4 pages (revtex) plus 1 figure (postscript). See also
http://vesta.physics.ucla.edu/~smolin/ . Replaced to correct interchanged
and near top of column 2, page
Violation of Bell's inequalities implies distillability for N qubits
We consider quantum systems composed of qubits, and the family of all
Bell's correlation inequalities for two two-valued measurements per site. We
show that if a -qubit state violates any of these inequalities, then
it is at least bipartite distillable. Indeed there exists a link between the
amount of Bell's inequality violation and the degree of distillability. Thus,
we strengthen the interpretation of Bell's inequalities as detectors of useful
entanglement.Comment: 6 pages, 3 figures, REVTEX. List of authors extended. Partially
rewritten, a rather qualitative explanation of the results. Conclusions
unchange
Sufficient conditions for three-particle entanglement and their tests in recent experiments
We point out a loophole problem in some recent experimental claims to produce
three-particle entanglement. The problem consists in the question whether
mixtures of two-particle entangled states might suffice to explain the
experimental data.
In an attempt to close this loophole, we review two sufficient conditions
that distinguish between N-particle states in which all N particles are
entangled to each other and states in which only M particles are entangled
(with M<N). It is shown that three recent experiments to obtain three-particle
entangled states (Bouwmeester et al., Pan et al., and Rauschenbeutel et al.) do
not meet these conditions. We conclude that the question whether these
experiments provide confirmation of three-particle entanglement remains
unresolved. We also propose modifications of the experiments that would make
such confirmation feasible.Comment: 16 page
Fast light, slow light, and phase singularities: a connection to generalized weak values
We demonstrate that Aharonov-Albert-Vaidman (AAV) weak values have a direct
relationship with the response function of a system, and have a much wider
range of applicability in both the classical and quantum domains than
previously thought. Using this idea, we have built an optical system, based on
a birefringent photonic crystal, with an infinite number of weak values. In
this system, the propagation speed of a polarized light pulse displays both
superluminal and slow light behavior with a sharp transition between the two
regimes. We show that this system's response possesses two-dimensional,
vortex-antivortex phase singularities. Important consequences for optical
signal processing are discussed.Comment: 9 pages, 4 figures, accepted in Physical Review Letters (2003
Jamming non-local quantum correlations
We present a possible scheme to tamper with non-local quantum correlations in
a way that is consistent with relativistic causality, but goes beyond quantum
mechanics. A non-local ``jamming" mechanism, operating within a certain
space-time window, would not violate relativistic causality and would not lead
to contradictory causal loops. The results presented in this Letter do not
depend on any model of how quantum correlations arise and apply to any jamming
mechanism.Comment: 10 pp, LaTe
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