250 research outputs found
Simulation of bipartite qudit correlations
We present a protocol to simulate the quantum correlations of an arbitrary
bipartite state, when the parties perform a measurement according to two
traceless binary observables. We show that bits of classical
communication is enough on average, where is the dimension of both systems.
To obtain this result, we use the sampling approach for simulating the quantum
correlations. We discuss how to use this method in the case of qudits.Comment: 7 page
How much measurement independence is needed in order to demonstrate nonlocality?
If nonlocality is to be inferred from a violation of Bell's inequality, an
important assumption is that the measurement settings are freely chosen by the
observers, or alternatively, that they are random and uncorrelated with the
hypothetical local variables. We study the case where this assumption is
weakened, so that measurement settings and local variables are at least
partially correlated. As we show, there is a connection between this type of
model and models which reproduce nonlocal correlations by allowing classical
communication between the distant parties, and a connection with models that
exploit the detection loophole. We show that even if Bob's choices are
completely independent, all correlations obtained from projective measurements
on a singlet can be reproduced, with the correlation (measured by mutual
information) between Alice's choice and local variables less than or equal to a
single bit.Comment: 5 pages, 1 figure. v2 Various improvements in presentation. Results
unchange
Non-Locality and Theories of Causation
The aim of the paper is to investigate the characterization of an unambiguous
notion of causation linking single space-llike separated events in EPR-Bell
frameworks. This issue is investigated in ordinary quantum mechanics, with some
hints to no collapse formulations of the theory such as Bohmian mechanics.Comment: Presented at the NATO Advanced Research Workshop on Modality,
Probability and Bell's Theorems, Cracow, Poland, August 19-23, 200
Causarum Investigatio and the Two Bell's Theorems of John Bell
"Bell's theorem" can refer to two different theorems that John Bell proved,
the first in 1964 and the second in 1976. His 1964 theorem is the
incompatibility of quantum phenomena with the joint assumptions of Locality and
Predetermination. His 1976 theorem is their incompatibility with the single
property of Local Causality. This is contrary to Bell's own later assertions,
that his 1964 theorem began with the assumption of Local Causality, even if not
by that name. Although the two Bell's theorems are logically equivalent, their
assumptions are not. Hence, the earlier and later theorems suggest quite
different conclusions, embraced by operationalists and realists, respectively.
The key issue is whether Locality or Local Causality is the appropriate notion
emanating from Relativistic Causality, and this rests on one's basic notion of
causation. For operationalists the appropriate notion is what is here called
the Principle of Agent-Causation, while for realists it is Reichenbach's
Principle of common cause. By breaking down the latter into even more basic
Postulates, it is possible to obtain a version of Bell's theorem in which each
camp could reject one assumption, happy that the remaining assumptions reflect
its weltanschauung. Formulating Bell's theorem in terms of causation is
fruitful not just for attempting to reconcile the two camps, but also for
better describing the ontology of different quantum interpretations and for
more deeply understanding the implications of Bell's marvellous work.Comment: 24 pages. Prepared for proceedings of the "Quantum [Un]speakables II"
conference (Vienna, 2014), to be published by Springe
Quantum Counterfactuals and Locality
Stapp's counterfactual argument for quantum nonlocality based upon a Hardy
entangled state is shown to be flawed. While he has correctly analyzed a
particular framework using the method of consistent histories, there are
alternative frameworks which do not support his argument. The framework
dependence of quantum counterfactual arguments, with analogs in classical
counterfactuals, vitiates the claim that nonlocal (superluminal) influences
exist in the quantum world. Instead it shows that counterfactual arguments are
of limited use for analyzing these questions.Comment: 8 pages, 1 PSTricks figur
Non-realism : deep thought or a soft option ?
The claim that the observation of a violation of a Bell inequality leads to
an alleged alternative between nonlocality and non-realism is annoying because
of the vagueness of the second term.Comment: 5 page
The Communication Cost of Simulating Bell Correlations
What classical resources are required to simulate quantum correlations? For
the simplest and most important case of local projective measurements on an
entangled Bell pair state, we show that exact simulation is possible using
local hidden variables augmented by just one bit of classical communication.
Certain quantum teleportation experiments, which teleport a single qubit,
therefore admit a local hidden variables model.Comment: 4 pages, 2 figures; reference adde
The local content of all pure two-qubit states
The (non-)local content in the sense of Elitzur, Popescu, and Rohrlich (EPR2)
[Phys. Lett. A 162, 25 (1992)] is a natural measure for the (non-)locality of
quantum states. Its computation is in general difficult, even in low
dimensions, and is one of the few open questions about pure two-qubit states.
We present a complete solution to this long-lasting problem.Comment: 9 pages, 3 figure
Bell Inequalities with Auxiliary Communication
What is the communication cost of simulating the correlations produced by
quantum theory? We generalize Bell inequalities to the setting of local
realistic theories augmented by a fixed amount of classical communication.
Suppose two parties choose one of M two-outcome measurements and exchange 1 bit
of information. We present the complete set of inequalities for M = 2, and the
complete set of inequalities for the joint correlation observable for M = 3. We
find that correlations produced by quantum theory satisfy both of these sets of
inequalities. One bit of communication is therefore sufficient to simulate
quantum correlations in both of these scenarios.Comment: 5 page
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