159 research outputs found
Proposed experiment to test the bounds of quantum correlations
Clauser-Horne-Shimony-Holt inequality can give values between the classical
bound, 2, and Tsirelson's bound, 2 \sqrt 2. However, for a given set of local
observables, there are values in this range which no quantum state can attain.
We provide the analytical expression for the corresponding bound for a
parametrization of the local observables introduced by Filipp and Svozil, and
describe how to experimentally trace it using a source of singlet states. Such
an experiment will be useful to identify the origin of the experimental errors
in Bell's inequality-type experiments and could be modified to detect
hypothetical correlations beyond those predicted by quantum mechanics.Comment: REVTeX4, 4 pages, 2 figure
Causality and Cirel'son bounds
An EPR-Bell type experiment carried out on an entangled quantum system can
produce correlations stronger than allowed by local realistic theories. However
there are correlations that are no-signaling and are more non local than the
quantum correlations. Here we show that any correlations more non local than
those achievable in an EPR-Bell type experiment necessarily allow -in the
context of the quantum formalism- both for signaling and for generation of
entanglement. We use our approach to rederive Cirel'son bound for the CHSH
expression, and we derive a new Cirel'son type bound for qutrits. We discuss in
detail the interpretation of our approach.Comment: 5 page
How much larger quantum correlations are than classical ones
Considering as distance between two two-party correlations the minimum number
of half local results one party must toggle in order to turn one correlation
into the other, we show that the volume of the set of physically obtainable
correlations in the Einstein-Podolsky-Rosen-Bell scenario is (3 pi/8)^2 = 1.388
larger than the volume of the set of correlations obtainable in local
deterministic or probabilistic hidden-variable theories, but is only 3 pi^2/32
= 0.925 of the volume allowed by arbitrary causal (i.e., no-signaling)
theories.Comment: REVTeX4, 6 page
Interconversion of Nonlocal Correlations
In this paper we study the correlations that arise when two separated parties
perform measurements on systems they hold locally. We restrict ourselves to
those correlations with which arbitrarily fast transmission of information is
impossible. These correlations are called nonsignaling. We allow the
measurements to be chosen from sets of an arbitrary size, but promise that each
measurement has only two possible outcomes. We find the structure of this
convex set of nonsignaling correlations by characterizing its extreme points.
Taking an information-theoretic view, we prove that all of these extreme
correlations are interconvertible. This suggests that the simplest extremal
nonlocal distribution (called a PR box) might be the basic unit of nonlocality.
We also show that this unit of nonlocality is sufficient to simulate all
quantum states when measured with two outcome measurements.Comment: 7 pages + appendix, single colum
Distilling Non-Locality
Two parts of an entangled quantum state can have a correlation in their joint
behavior under measurements that is unexplainable by shared classical
information. Such correlations are called non-local and have proven to be an
interesting resource for information processing. Since non-local correlations
are more useful if they are stronger, it is natural to ask whether weak
non-locality can be amplified. We give an affirmative answer by presenting the
first protocol for distilling non-locality in the framework of generalized
non-signaling theories. Our protocol works for both quantum and non-quantum
correlations. This shows that in many contexts, the extent to which a single
instance of a correlation can violate a CHSH inequality is not a good measure
for the usefulness of non-locality. A more meaningful measure follows from our
results.Comment: Revised abstract, introduction and conclusion. Accepted by PR
Can one see entanglement ?
The human eye can detect optical signals containing only a few photons. We
investigate the possibility to demonstrate entanglement with such biological
detectors. While one person could not detect entanglement by simply observing
photons, we discuss the possibility for several observers to demonstrate
entanglement in a Bell-type experiment, in which standard detectors are
replaced by human eyes. Using a toy model for biological detectors that
captures their main characteristic, namely a detection threshold, we show that
Bell inequalities can be violated, thus demonstrating entanglement. Remarkably,
when the response function of the detector is close to a step function, quantum
non-locality can be demonstrated without any further assumptions. For smoother
response functions, as for the human eye, post-selection is required.Comment: 5 pages, 5 figure
Maximal violation of the I3322 inequality using infinite dimensional quantum systems
The I3322 inequality is the simplest bipartite two-outcome Bell inequality
beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three
two-outcome measurements per party. In case of the CHSH inequality the maximal
quantum violation can already be attained with local two-dimensional quantum
systems, however, there is no such evidence for the I3322 inequality. In this
paper a family of measurement operators and states is given which enables us to
attain the largest possible quantum value in an infinite dimensional Hilbert
space. Further, it is conjectured that our construction is optimal in the sense
that measuring finite dimensional quantum systems is not enough to achieve the
true quantum maximum. We also describe an efficient iterative algorithm for
computing quantum maximum of an arbitrary two-outcome Bell inequality in any
given Hilbert space dimension. This algorithm played a key role to obtain our
results for the I3322 inequality, and we also applied it to improve on our
previous results concerning the maximum quantum violation of several bipartite
two-outcome Bell inequalities with up to five settings per party.Comment: 9 pages, 3 figures, 1 tabl
Lower bounds on the entanglement needed to play XOR non-local games
We give an explicit family of XOR games with O(n)-bit questions requiring 2^n
ebits to play near-optimally. More generally we introduce a new technique for
proving lower bounds on the amount of entanglement required by an XOR game: we
show that near-optimal strategies for an XOR game G correspond to approximate
representations of a certain C^*-algebra associated to G. Our results extend an
earlier theorem of Tsirelson characterising the set of quantum strategies which
implement extremal quantum correlations.Comment: 20 pages, no figures. Corrected abstract, body of paper unchange
Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
Quantum theory imposes a strict limit on the strength of non-local
correlations. It only allows for a violation of the CHSH inequality up to the
value 2 sqrt(2), known as Tsirelson's bound. In this note, we consider
generalized CHSH inequalities based on many measurement settings with two
possible measurement outcomes each. We demonstrate how to prove Tsirelson
bounds for any such generalized CHSH inequality using semidefinite programming.
As an example, we show that for any shared entangled state and observables
X_1,...,X_n and Y_1,...,Y_n with eigenvalues +/- 1 we have | + <X_2
Y_1> + + + ... + - | <= 2 n
cos(pi/(2n)). It is well known that there exist observables such that equality
can be achieved. However, we show that these are indeed optimal. Our approach
can easily be generalized to other inequalities for such observables.Comment: 9 pages, LateX, V2: Updated reference [3]. To appear in Physical
Review
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