2,143 research outputs found
Bipartite Bell Inequality and Maximal Violation
We present new bell inequalities for arbitrary dimensional bipartite quantum
systems. The maximal violation of the inequalities is computed. The Bell
inequality is capable of detecting quantum entanglement of both pure and mixed
quantum states more effectively.Comment: 6 pages,no figure
A generalized structure of Bell inequalities for bipartite arbitrary dimensional systems
We propose a generalized structure of Bell inequalities for arbitrary
d-dimensional bipartite systems, which includes the existing two types of Bell
inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev.
Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)].
We analyze Bell inequalities in terms of correlation functions and joint
probabilities, and show that the coefficients of correlation functions and
those of joint probabilities are in Fourier transform relations. We finally
show that the coefficients in the generalized structure determine the
characteristics of quantum violation and tightness.Comment: 6 pages, 1 figur
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
D-outcome measurement for a nonlocality test
For the purpose of the nonlocality test, we propose a general correlation
observable of two parties by utilizing local -outcome measurements with
SU() transformations and classical communications. Generic symmetries of the
SU() transformations and correlation observables are found for the test of
nonlocality. It is shown that these symmetries dramatically reduce the number
of numerical variables, which is important for numerical analysis of
nonlocality. A linear combination of the correlation observables, which is
reduced to the Clauser-Horne-Shimony-Holt (CHSH) Bell's inequality for two
outcome measurements, is led to the Collins-Gisin-Linden-Massar-Popescu (CGLMP)
nonlocality test for -outcome measurement. As a system to be tested for its
nonlocality, we investigate a continuous-variable (CV) entangled state with
measurement outcomes. It allows the comparison of nonlocality based on
different numbers of measurement outcomes on one physical system. In our
example of the CV state, we find that a pure entangled state of any degree
violates Bell's inequality for measurement outcomes when the
observables are of SU() transformations.Comment: 16 pages, 2 figure
Better Bell Inequality Violation by Collective Measurements
The standard Bell inequality experiments test for violation of local realism
by repeatedly making local measurements on individual copies of an entangled
quantum state. Here we investigate the possibility of increasing the violation
of a Bell inequality by making collective measurements. We show that
nonlocality of bipartite pure entangled states, quantified by their maximal
violation of the Bell-Clauser-Horne inequality, can always be enhanced by
collective measurements, even without communication between the parties. For
mixed states we also show that collective measurements can increase the
violation of Bell inequalities, although numerical evidence suggests that the
phenomenon is not common as it is for pure states.Comment: 7 pages, 4 figures and 1 table; references update
Inequalities Detecting Quantum Entanglement for Systems
We present a set of inequalities for detecting quantum entanglement of
quantum states. For and systems, the
inequalities give rise to sufficient and necessary separability conditions for
both pure and mixed states. For the case of , these inequalities are
necessary conditions for separability, which detect all entangled states that
are not positive under partial transposition and even some entangled states
with positive partial transposition. These inequalities are given by mean
values of local observables and present an experimental way of detecting the
quantum entanglement of quantum states and even multi-qubit pure
states.Comment: 6 page
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