45 research outputs found
On local-hidden-variable no-go theorems
The strongest attack against quantum mechanics came in 1935 in the form of a
paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum
mechanics could not be called a complete theory of Nature, for every element of
reality is not represented in the formalism as such. The authors then put forth
a proposition: we must search for a theory where, upon knowing everything about
the system, including possible hidden variables, one could make precise
predictions concerning elements of reality. This project was ultimatly doomed
in 1964 with the work of Bell Bell, who showed that the most general local
hidden variable theory could not reproduce correlations that arise in quantum
mechanics. There exist mainly three forms of no-go theorems for local hidden
variable theories. Although almost every physicist knows the consequences of
these no-go theorems, not every physicist is aware of the distinctions between
the three or even their exact definitions. Thus we will discuss here the three
principal forms of no-go theorems for local hidden variable theories of Nature.
We will define Bell inequalities, Bell inequalities without inequalities and
pseudo-telepathy. A discussion of the similarities and differences will follow.Comment: 7 pages, no figure, replaced "Bell inequalities" with "Bell theorems"
and updated the reference
Characterization of Binary Constraint System Games
We consider a class of nonlocal games that are related to binary constraint
systems (BCSs) in a manner similar to the games implicit in the work of Mermin
[N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems,"
Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary
variables and m constraints. We show that, whenever there is a perfect
entangled protocol for such a game, there exists a set of binary observables
with commutations and products similar to those exhibited by Mermin. We also
show how to derive upper bounds strictly below 1 for the the maximum entangled
success probability of some BCS games. These results are partial progress
towards a larger project to determine the computational complexity of deciding
whether a given instance of a BCS game admits a perfect entangled strategy or
not.Comment: Revised version corrects an error in the previous version of the
proof of Theorem 1 that arises in the case of POVM measurement
Qubits from Number States and Bell Inequalities for Number Measurements
Bell inequalities for number measurements are derived via the observation
that the bits of the number indexing a number state are proper qubits.
Violations of these inequalities are obtained from the output state of the
nondegenerate optical parametric amplifier.Comment: revtex4, 7 pages, v2: results identical but extended presentation,
v3: published versio
Two qubits of a W state violate Bell's inequality beyond Cirel'son's bound
It is shown that the correlations between two qubits selected from a trio
prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more
than the correlations between two qubits in any quantum state. Such a violation
beyond Cirel'son's bound is smaller than the one achieved by two qubits
selected from a trio in a Greenberger-Horne-Zeilinger state [A. Cabello, Phys.
Rev. Lett. 88, 060403 (2002)]. However, it has the advantage that all local
observers can know from their own measurements whether their qubits belongs or
not to the selected pair.Comment: REVTeX4, 5 page
Maximal Violation of Bell Inequalities using Continuous Variables Measurements
We propose a whole family of physical states that yield a violation of the
Bell CHSH inequality arbitrarily close to its maximum value, when using
quadrature phase homodyne detection. This result is based on a new binning
process called root binning, that is used to transform the continuous variables
measurements into binary results needed for the tests of quantum mechanics
versus local realistic theories. A physical process in order to produce such
states is also suggested. The use of high-efficiency spacelike separated
homodyne detections with these states and this binning process would result in
a conclusive loophole-free test of quantum mechanics.Comment: 7 pages, 5 figures, to appear in PRA in a slightly different versio
A Zoology of Bell inequalities resistant to detector inefficiency
We derive both numerically and analytically Bell inequalities and quantum
measurements that present enhanced resistance to detector inefficiency. In
particular we describe several Bell inequalities which appear to be optimal
with respect to inefficient detectors for small dimensionality d=2,3,4 and 2 or
more measurement settings at each side. We also generalize the family of Bell
inequalities described in Collins et all (Phys. Rev. Lett. 88, 040404) to take
into account the inefficiency of detectors. In addition we consider the
possibility for pairs of entangled particles to be produced with probability
less than one. We show that when the pair production probability is small, one
must in general use different Bell inequalities than when the pair production
probability is high.Comment: 12 pages, revtex. Appendix completed, minor revision
Relations between entanglement, Bell-inequality violation and teleportation fidelity for the two-qubit X states
Based on the assumption that the receiver Bob can apply any unitary
transformation, Horodecki {\it et al.} [Phys. Lett. A {\bf 222}, 21 (1996)]
proved that any mixed two spin-1/2 state which violates the Bell-CHSH
inequality is useful for teleportation. Here, we further show that any X state
which violates the Bell-CHSH inequality can also be used for nonclassical
teleportation even if Bob can only perform the identity or the Pauli rotation
operations. Moreover, we showed that the maximal difference between the two
average fidelities achievable via Bob's arbitrary transformations and via the
sole identity or the Pauli rotation is 1/9.Comment: 5 pages, to be published in "Quantum Information Processing
Polarization Correlations of 1S0 Proton Pairs as Tests of Bell and Wigner Inequalities
In an experiment designed to overcome the loophole of observer dependent
reality and satisfying the counterfactuality condition, we measured
polarization correlations of 1S0 proton pairs produced in 12C(d,2He) and
1H(d,He) reactions in one setting. The results of these measurements are used
to test the Bell and Wigner inequalties against the predictions of quantum
mechanics.Comment: 8 pages, 4 figure
Revealing Bell's Nonlocality for Unstable Systems in High Energy Physics
Entanglement and its consequences - in particular the violation of Bell
inequalities, which defies our concepts of realism and locality - have been
proven to play key roles in Nature by many experiments for various quantum
systems. Entanglement can also be found in systems not consisting of ordinary
matter and light, i.e. in massive meson--antimeson systems. Bell inequalities
have been discussed for these systems, but up to date no direct experimental
test to conclusively exclude local realism was found. This mainly stems from
the fact that one only has access to a restricted class of observables and that
these systems are also decaying. In this Letter we put forward a Bell
inequality for unstable systems which can be tested at accelerator facilities
with current technology. Herewith, the long awaited proof that such systems at
different energy scales can reveal the sophisticated "dynamical" nonlocal
feature of Nature in a direct experiment gets feasible. Moreover, the role of
entanglement and CP violation, an asymmetry between matter and antimatter, is
explored, a special feature offered only by these meson-antimeson systems.Comment: 6 pages, 3 figure
Dynamics of entanglement between two trapped atoms
We investigate the dynamics of entanglement between two continuous variable
quantum systems. The model system consists of two atoms in a harmonic trap
which are interacting by a simplified s-wave scattering. We show, that the
dynamically created entanglement changes in a steplike manner. Moreover, we
introduce local operators which allow us to violate a Bell-CHSH inequality
adapted to the continuous variable case. The correlations show nonclassical
behavior and almost reach the maximal quantum mechanical value. This is
interesting since the states prepared by this interaction are very different
from any EPR-like state.Comment: 9 page