2,024 research outputs found
On Hardness of the Joint Crossing Number
The Joint Crossing Number problem asks for a simultaneous embedding of two
disjoint graphs into one surface such that the number of edge crossings
(between the two graphs) is minimized. It was introduced by Negami in 2001 in
connection with diagonal flips in triangulations of surfaces, and subsequently
investigated in a general form for small-genus surfaces. We prove that all of
the commonly considered variants of this problem are NP-hard already in the
orientable surface of genus 6, by a reduction from a special variant of the
anchored crossing number problem of Cabello and Mohar
Bell's theorem without inequalities and without alignments
A proof of Bell's theorem without inequalities is presented which exhibits
three remarkable properties: (a) reduced local states are immune to collective
decoherence; (b) distant local setups do not need to be aligned, since the
required perfect correlations are achieved for any local rotation of the local
setups; (c) local measurements require only individual measurements on the
qubits. Indeed, it is shown that this proof is essentially the only one which
fulfils (a), (b), and (c).Comment: REVTeX4, 4 page
Mermin inequalities for perfect correlations
Any n-qubit state with n independent perfect correlations is equivalent to a
graph state. We present the optimal Bell inequalities for perfect correlations
and maximal violation for all classes of graph states with n < 7 qubits. Twelve
of them were previously unknown and four give the same violation as the
Greenberger-Horne-Zeilinger state, although the corresponding states are more
resistant to decoherence.Comment: REVTeX4, 5 pages, 1 figur
Enhancing the Violation of the Einstein-Podolsky-Rosen Local Realism by Quantum Hyper-entanglement
Mermin's observation [Phys. Rev. Lett. {\bf 65}, 1838 (1990)] that the
magnitude of the violation of local realism, defined as the ratio between the
quantum prediction and the classical bound, can grow exponentially with the
size of the system is demonstrated using two-photon hyper-entangled states
entangled in polarization and path degrees of freedom, and local measurements
of polarization and path simultaneously.Comment: Minor errors corrected. To appear on Physical Review Letter
Stronger two-observer all-versus-nothing violation of local realism
We introduce a two-observer all-versus-nothing proof of Bell's theorem which
reduces the number of required quantum predictions from 9 [A. Cabello, Phys.
Rev. Lett. 87, 010403 (2001); Z.-B. Chen et al., Phys. Rev. Lett. 90, 160408
(2003)] to 4, provides a greater amount of evidence against local realism,
reduces the detection efficiency requirements for a conclusive experimental
test of Bell's theorem, and leads to a Bell's inequality which resembles
Mermin's inequality for three observers [N. D. Mermin, Phys. Rev. Lett. 65,
1838 (1990)] but requires only two observers.Comment: REVTeX4, 5 page
The Complexity of Separating Points in the Plane
We study the following separation problem: given n connected curves and two points s and t in the plane, compute the minimum number of curves one needs to retain so that any path connecting s to t intersects some of the retained curves. We give the first polynomial (O(n3)) time algorithm for the problem, assuming that the curves have reasonable computational properties. The algorithm is based on considering the intersection graph of the curves, defining an appropriate family of closed walks in the intersection graph that satisfies the 3-path-condition, and arguing that a shortest cycle in the family gives an optimal solution. The 3-path-condition has been used mainly in topological graph theory, and thus its use here makes the connection to topology clear. We also show that the generalized version, where several input points are to be separated, is NP-hard for natural families of curves, like segments in two directions or unit circles
Multiparty multilevel Greenberger-Horne-Zeilinger states
The proof of Bell's theorem without inequalities by Greenberger, Horne, and
Zeilinger (GHZ) is extended to multiparticle multilevel systems. The proposed
procedure generalizes previous partial results and provides an operational
characterization of the so-called GHZ states for multiparticle multilevel
systems.Comment: REVTeX, 5 pages, 1 figur
The generalized Kochen-Specker theorem
A proof of the generalized Kochen-Specker theorem in two dimensions due to
Cabello and Nakamura is extended to all higher dimensions. A set of 18 states
in four dimensions is used to give closely related proofs of the generalized
Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the
relationship between these three theorems.Comment: 5 pages, 1 Table. A new third paragraph and an additional reference
have been adde
State-independent quantum violation of noncontextuality in four dimensional space using five observables and two settings
Recently, a striking experimental demonstration [G. Kirchmair \emph{et al.},
Nature, \textbf{460}, 494(2009)] of the state-independent quantum mechanical
violation of non-contextual realist models has been reported for any two-qubit
state using suitable choices of \emph{nine} product observables and \emph{six}
different measurement setups. In this report, a considerable simplification of
such a demonstration is achieved by formulating a scheme that requires only
\emph{five} product observables and \emph{two} different measurement setups. It
is also pointed out that the relevant empirical data already available in the
experiment by Kirchmair \emph{et al.} corroborate the violation of the NCR
models in accordance with our proof
Finding Multiple New Optimal Locations in a Road Network
We study the problem of optimal location querying for location based services
in road networks, which aims to find locations for new servers or facilities.
The existing optimal solutions on this problem consider only the cases with one
new server. When two or more new servers are to be set up, the problem with
minmax cost criteria, MinMax, becomes NP-hard. In this work we identify some
useful properties about the potential locations for the new servers, from which
we derive a novel algorithm for MinMax, and show that it is efficient when the
number of new servers is small. When the number of new servers is large, we
propose an efficient 3-approximate algorithm. We verify with experiments on
real road networks that our solutions are effective and attains significantly
better result quality compared to the existing greedy algorithms
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