On Classical Teleportation and Classical Nonlocality

An interesting protocol for classical teleportation of an unknown classical state was recently suggested by Cohen, and by Gour and Meyer. In that protocol, Bob can sample from a probability distribution P that is given to Alice, even if Alice has absolutely no knowledge about P. Pursuing a similar line of thought, we suggest here a limited form of nonlocality - "classical nonlocality". Our nonlocality is the (somewhat limited) classical analogue of the Hughston-Jozsa-Wootters (HJW) quantum nonlocality. The HJW nonlocality tells us how, for a given density matrix rho, Alice can generate any rho-ensemble on the North Star. This is done using surprisingly few resources - one shared entangled state (prepared in advance), one generalized quantum measurement, and no communication. Similarly, our classical nonlocality presents how, for a given probability distribution P, Alice can generate any P-ensemble on the North Star, using only one correlated state (prepared in advance), one (generalized) classical measurement, and no communication. It is important to clarify that while the classical teleportation and the classical non-locality protocols are probably rather insignificant from a classical information processing point of view, they significantly contribute to our understanding of what exactly is quantum in their well established and highly famous quantum analogues.Comment: 8 pages, Version 2 is using the term "quantum remote steering" to describe HJW idea, and "classical remote steering" is the main new result of this current paper. Version 2 also has an additional citation (to Gisin's 89 paper

Is higher-order evidence evidence?

Suppose we learn that we have a poor track record in forming beliefs rationally, or that a brilliant colleague thinks that we believe P irrationally. Does such input require us to revise those beliefs whose rationality is in question? When we gain information suggesting that our beliefs are irrational, we are in one of two general cases. In the first case we made no error, and our beliefs are rational. In that case the input to the contrary is misleading. In the second case we indeed believe irrationally, and our original evidence already requires us to fix our mistake. In that case the input to that effect is normatively superfluous. Thus, we know that information suggesting that our beliefs are irrational is either misleading or superfluous. This, I submit, renders the input incapable of justifying belief revision, despite our not knowing which of the two kinds it is

The Signature of Microlensing in QSO Variability-Redshift Correlations

A recently discovered inverse correlation between QSO redshift and long-term continuum variability timescales was suggested to be the signature of microlensing on cosmological scales (Hawkins 1993). A general theoretical method for calculating such correlations is presented and applied to various lensing scenarios in the framework of $\Lambda = 0$ Friedmann cosmologies. It is shown that the observed timescales can be strongly influenced by the observational limitations: the finite duration of the monitoring campaign and the finite photometric sensitivity. In most scenarios the timescales increase with source redshift, $z_s$, although slower than the $1+z_s$ time dilation expected of intrinsic variability. A decrease can be obtained for an extended source observed with moderate sensitivity. In this case, only lenses no further away than several hundreds Mpc participate in the lensing. The resulting optical depth is too small to explain the common long-term QSO variability unless an extremely high local lens density is assumed. These results do not support the idea that the reported inverse correlation can be attributed to microlensing of a uniform QSO sample by a uniform distribution of lenses. The possibility of using observations at various wavelengths and QSO samples at various positions to identify microlensing in QSO variability is also discussed.Comment: Self-unpacking, uuencoded postscript file, 10 pages with 7 figures included. Accepted for publication by the MNRAS