2,181 research outputs found
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
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
Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
If we distribute n qubits between two parties, which quantum pure states and
distributions of qubits would allow all-versus-nothing (or
Greenberger-Horne-Zeilinger-like) proofs of Bell's theorem using only
single-qubit measurements? We show a necessary and sufficient condition for the
existence of these proofs for any number of qubits, and provide all distinct
proofs up to n=7 qubits. Remarkably, there is only one distribution of a state
of n=4 qubits, and six distributions, each for a different state of n=6 qubits,
which allow these proofs.Comment: REVTeX4, 4 pages, 2 figure
Efficient and weak efficient points in vector optimization with generalized cone convexity
AbstractIn this paper, we present necessary and sufficient conditions of efficiency and weak efficiency under generalized cone-convexity and cone-subconvexity. The results are stated in partially ordered real linear spaces from a separation theorem between convex cones which need not be solid
Six-qubit permutation-based decoherence-free orthogonal basis
There is a natural orthogonal basis of the 6-qubit decoherence-free (DF)
space robust against collective noise. Interestingly, most of the basis states
can be obtained from one another just permuting qubits. This property: (a) is
useful for encoding qubits in DF subspaces, (b) allows the implementation of
the Bennett-Brassard 1984 (BB84) protocol in DF subspaces just permuting
qubits, which completes a the method for quantum key distribution using DF
states proposed by Boileau et al. [Phys. Rev. Lett. 92, 017901 (2004)], and (c)
points out that there is only one 6-qubit DF state which is essentially new
(not obtained by permutations) and therefore constitutes an interesting
experimental challenge.Comment: REVTeX4, 5 page
Bipartite Bell inequalities for hyperentangled states
We show that bipartite Bell inequalities based on the Einstein-Podolsky-Rosen
criterion for elements of reality and derived from the properties of some
hyperentangled states allow feasible experimental verifications of the fact
that quantum nonlocality grows exponentially with the size of the subsystems,
and Bell loophole-free tests with currently available photodetection
efficiencies.Comment: REVTeX4, 5 page
Compact set of invariants characterizing graph states of up to eight qubits
The set of entanglement measures proposed by Hein, Eisert, and Briegel for
n-qubit graph states [Phys. Rev. A 69, 062311 (2004)] fails to distinguish
between inequivalent classes under local Clifford operations if n > 6. On the
other hand, the set of invariants proposed by van den Nest, Dehaene, and De
Moor (VDD) [Phys. Rev. A 72, 014307 (2005)] distinguishes between inequivalent
classes, but contains too many invariants (more than 2 10^{36} for n=7) to be
practical. Here we solve the problem of deciding which entanglement class a
graph state of n < 9 qubits belongs to by calculating some of the state's
intrinsic properties. We show that four invariants related to those proposed by
VDD are enough for distinguishing between all inequivalent classes with n < 9
qubits.Comment: REVTeX4, 9 pages, 1 figur
Loophole-free Bell's experiment and two-photon all-versus-nothing violation of local realism
We introduce an all-versus-nothing proof of impossibility of
Einstein-Podolsky-Rosen's local elements of reality for two photons entangled
both in polarization and path degrees of freedom, which leads to a Bell's
inequality where the classical bound is 8 and the quantum prediction is 16. A
simple estimation of the detection efficiency required to close the detection
loophole using this proof gives eta > 0.69. This efficiency is lower than that
required for previous proposals.Comment: REVTeX4, 4 page
N-particle N-level singlet states: Some properties and applications
Three apparently unrelated problems which have no solution using classical
tools are described: the "N-strangers," "secret sharing," and "liar detection"
problems. A solution for each of them is proposed. Common to all three
solutions is the use of quantum states of total spin zero of N spin-(N-1)/2
particles.Comment: REVTeX4, 4 pages, 1 figur
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