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 $\log(d)$ bits of classical communication is enough on average, where $d$ 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