A brief review of the attempts to define “elements of reality” in the framework of quantum theory is presented. It is noted that most definitions of elements of reality have in common the feature to be a definite outcome of some measurement. Elements of reality are extended to pre- and post- selected systems and to measurements which fulfill certain criteria of weakness of the coupling. Some features of the newly introduced concepts are discussed.

A clear and accessible presentation of quantum theory, suitable for researchers yet accessible to graduates.

An apparent paradox proposed by Aharonov and Vaidman in which a single particle can be found with certainty in two (or more) boxes is analyzed by way of a simple thought experiment. It is found that the apparent paradox arises from an invalid counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule and effectively attributes conflicting properties not to the same particle but no different particles. A connection is made between the present analysis and the consistent histories formulation of Griffiths. Finally, a (...) critique is given of some recent counterarguments by Vaidman against the rejection of the counterfactual usage of the ABL rule. (shrink)

This paper is an answer to the preceding paper by Kastner, in which she continued the criticism of the counterfactual usage of the Aharonov-Bergman-Lebowitz rule in the framework of the time-symmetrized quantum theory, in particular, by analyzing the three-box “paradox.” It is argued that the criticism is not sound. Paradoxical features of the three-box example are discussed. It is explained that the elements of reality in the framework of time-symmetrized quantum theory are counterfactual statements, and therefore, even conflicting elements of (...) reality can be associated with a single system. It is shown how such “counterfactual” elements of reality can be useful in the analysis of a physical experiment (the three-box example). The validity of Kastner's application of the consistent histories approach to the time-symmetrized counterfactuals is questioned. (shrink)

Special relativity is most naturally formulated as a theory of spacetime geometry, but within the spacetime framework probability appears to be a purely epistemic notion. It is possible that progress can be made with rather different approaches - covariant stochastic equations, in particular - but the results to date are not encouraging. However, it seems a non-epistemic notion of probability can be made out in Minkowski space on Everett's terms. I shall work throughout with the consistent histories formalism. I shall (...) start with a conservative interpretation, and then go on to Everett's. (shrink)

A quantum key distribution scheme whose security depends on the features of pre- and post-selected quantum states is described.