19 research outputs found
A tight Tsirelson inequality for infinitely many outcomes
We present a novel tight bound on the quantum violations of the CGLMP
inequality in the case of infinitely many outcomes. Like in the case of
Tsirelson's inequality the proof of our new inequality does not require any
assumptions on the dimension of the Hilbert space or kinds of operators
involved. However, it is seen that the maximal violation is obtained by the
conjectured best measurements and a pure, but not maximally entangled, state.
We give an approximate state which, in the limit where the number of outcomes
tends to infinity, goes to the optimal state for this setting. This state might
be potentially relevant for experimental verifications of Bell inequalities
through multi-dimenisonal entangled photon pairs.Comment: 5 pages, 2 figures; improved presentation, change in title, as
published
Experimental violation of a spin-1 Bell inequality using maximally-entangled four-photon states
We demonstrate the first experimental violation of a spin-1 Bell inequality.
The spin-1 inequality is a calculation based on the Clauser, Horne, Shimony and
Holt formalism. For entangled spin-1 particles the maximum quantum mechanical
prediction is 2.552 as opposed to a maximum of 2, predicted using local hidden
variables. We obtained an experimental value of 2.27 using the
four-photon state generated by pulsed, type-II, stimulated parametric
down-conversion. This is a violation of the spin-1 Bell inequality by more than
13 standard deviations.Comment: 5 pages, 3 figures, Revtex4. Problem with figures resolve
Generalizing Tsirelson's bound on Bell inequalities using a min-max principle
Bounds on the norm of quantum operators associated with classical Bell-type
inequalities can be derived from their maximal eigenvalues. This quantitative
method enables detailed predictions of the maximal violations of Bell-type
inequalities.Comment: 4 pages, 2 figures, RevTeX4, replaced with published versio
Bayesian Nash Equilibria and Bell Inequalities
Games with incomplete information are formulated in a multi-sector
probability matrix formalism that can cope with quantum as well as classical
strategies. An analysis of classical and quantum strategy in a multi-sector
extension of the game of Battle of Sexes clarifies the two distinct roles of
nonlocal strategies, and establish the direct link between the true quantum
gain of game's payoff and the breaking of Bell inequalities.Comment: 6 pages, LaTeX JPSJ 2 column format, changes in sections 1, 3 and 4,
added reference
Optimal eavesdropping in quantum cryptography with six states
A generalization of the quantum cryptographic protocol by Bennett and
Brassard is discussed, using three conjugate bases, i.e. six states. By
calculating the optimal mutual information between sender and eavesdropper it
is shown that this scheme is safer against eavesdropping on single qubits than
the one based on two conjugate bases. We also address the question for a
connection between the maximal classical correlation in a generalized Bell
inequality and the intersection of mutual informations between sender/receiver
and sender/eavesdropper.Comment: 4 pages, 1 figur
Violating Bell's inequality beyond Cirel'son's bound
Cirel'son inequality states that the absolute value of the combination of
quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH)
inequality is bound by . It is shown that the correlations of two
qubits belonging to a three-qubit system can violate the CHSH inequality beyond
. Such a violation is not in conflict with Cirel'son's inequality
because it is based on postselected systems. The maximum allowed violation of
the CHSH inequality, 4, can be achieved using a Greenberger-Horne-Zeilinger
state.Comment: REVTeX4, 4 page
Quantum Communication between N partners and Bell's inequalities
We consider a family of quantum communication protocols involving
partners. We demonstrate the existence of a link between the security of these
protocols against individual attacks by the eavesdropper, and the violation of
some Bell's inequalities, generalizing the link that was noticed some years ago
for two-partners quantum cryptography. The arguments are independent of the
local hidden variable debate.Comment: 4 pages, 2 figure
Maximal Violation of Bell's Inequalities for Continuous Variable Systems
We generalize Bell's inequalities to biparty systems with continuous quantum
variables. This is achieved by introducing the Bell operator in perfect analogy
to the usual spin-1/2 systems. It is then demonstrated that two-mode squeezed
vacuum states display quantum nonlocality by using the generalized Bell
operator. In particular, the original Einstein-Podolsky-Rosen entangled states,
which are the limiting case of the two-mode squeezed vacuum states, can
maximally violate Bell's inequality due to Clauser, Horne, Shimony and Holt.
The experimental aspect of our scheme and nonlocality of arbitrary biparticle
entangled pure states of continuous variables are briefly considered.Comment: RevTEX, 4 pages, no figure. An important note was adde
Violations of local realism by two entangled quNits are stronger than for two qubits
Tests of local realism vs quantum mechanics based on Bell's inequality employ
two entangled qubits. We investigate the general case of two entangled quNits,
i.e. quantum systems defined in an N-dimensional Hilbert space. Via a numerical
linear optimization method we show that violations of local realism are
stronger for two maximally entangled quNits (N=3,4,...,9), than for two qubits
and that they increase with N. The two quNit measurements can be experimentally
realized using entangled photons and unbiased multiport beamsplitters.Comment: 5 pages, 2 pictures, LaTex, two columns; No changes in the result
Quantum Matching Pennies Game
A quantum version of the Matching Pennies (MP) game is proposed that is
played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct
the quantum game without using the state vectors, while considering only the
quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We
embed the classical game within the quantum game such that the classical MP
game results when the quantum mechanical joint probabilities become
factorizable. We report new Nash equilibria in the quantum MP game that emerge
when the quantum mechanical joint probabilities maximally violate the
Clauser-Horne-Shimony-Holt form of Bell's inequality.Comment: Revised in light of referees' comments, submitted to Journal of the
Physical Society of Japan, 14 pages, 1 figur