41 research outputs found
Bell inequality, Bell states and maximally entangled states for n qubits
First, we present a Bell type inequality for n qubits, assuming that m out of
the n qubits are independent. Quantum mechanics violates this inequality by a
ratio that increases exponentially with m. Hence an experiment on n qubits
violating of this inequality sets a lower bound on the number m of entangled
qubits. Next, we propose a definition of maximally entangled states of n
qubits. For this purpose we study 5 different criteria. Four of these criteria
are found compatible. For any number n of qubits, they determine an orthogonal
basis consisting of maximally entangled states generalizing the Bell states.Comment: 8 pages, no figur
On the power of non-local boxes
A non-local box is a virtual device that has the following property: given
that Alice inputs a bit at her end of the device and that Bob does likewise, it
produces two bits, one at Alice's end and one at Bob's end, such that the XOR
of the outputs is equal to the AND of the inputs. This box, inspired from the
CHSH inequality, was first proposed by Popescu and Rohrlich to examine the
question: given that a maximally entangled pair of qubits is non-local, why is
it not maximally non-local? We believe that understanding the power of this box
will yield insight into the non-locality of quantum mechanics. It was shown
recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able
to simulate correlations from any measurement on a singlet state. Here, we show
that the non-local box can in fact do much more: through the simulation of the
magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we
show that the non-local box can simulate quantum correlations that no entangled
pair of qubits can in a bipartite scenario and even in a multi-party scenario.
Finally we show that a single non-local box cannot simulate all quantum
correlations and propose a generalization for a multi-party non-local box. In
particular, we show quantum correlations whose simulation requires an
exponential amount of non-local boxes, in the number of maximally entangled
qubit pairs.Comment: 14 pages, 1 figur
Optimization of Bell's Inequality Violation For Continuous Variable Systems
Two mode squeezed vacuum states allow Bell's inequality violation (BIQV) for
all non-vanishing squeezing parameter . Maximal violation occurs at
when the parity of either component averages to zero. For a
given entangled {\it two spin} system BIQV is optimized via orientations of the
operators entering the Bell operator (cf. S. L. Braunstein, A. Mann and M.
Revzen: Phys. Rev. Lett. {\bf68}, 3259 (1992)). We show that for finite
in continuous variable systems (and in general whenever the dimensionality of
the subsystems is greater than 2) additional parameters are present for
optimizing BIQV. Thus the expectation value of the Bell operator depends, in
addition to the orientation parameters, on configuration parameters.
Optimization of these configurational parameters leads to a unique maximal BIQV
that depends only on The configurational parameter variation is used
to show that BIQV relation to entanglement is, even for pure state, not
monotonic.Comment: An example added; shows that the amount of Bell's inequality
violation as a measure of entanglement is doubtfu
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
Maximal Bell's Inequality Violation for Non Maximal Entanglement
Bell's inequality violation (BIQV) for correlations of polarization is
studied for a {\it product} state of two two-mode squeezed vacuum (TMSV)
states. The violation allowed is shown to attain its maximal limit for all
values of the squeezing parameter, . We show via an explicit example
that a state whose entanglement is not maximal allow maximal BIQV. The Wigner
function of the state is non negative and the average value of either
polarization is nil.Comment: 8 pages, latex, no figure
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
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
The Problem of Contextuality and the Impossibility of Experimental Metaphysics Thereof
Recently a new impulse has been given to the experimental investigation of
contextuality. In this paper we show that for a widely used definition of
contextuality there can be no decisive experiment on the existence of
contextuality. To this end, we give a clear presentation of the hidden variable
models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the
Kochen-Specker Theorem. Although we disagree with this last statement, the
models play a significant role in the discussion on the meaning of
contextuality. In fact, we introduce a specific MKC-model of which we show that
it is non-contextual and completely in agreement with quantum mechanical
predictions. We also investigate the possibility of other definitions of
non-contextuality --with an emphasis on operational definitions-- and argue
that any useful definition relies on the specification of a theoretical
framework. It is therefore concluded that no experimental test can yield any
conclusions about contextuality on a metaphysical level
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
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