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An experimental test of the "special state" theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern-Gerlach setup. The "special state" theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this article background material is given on both quantum measurement and statistical mechanics aspects. For example, it is shown that future boundary conditions would not contradict experience, indicating that the fundamental equal-a-priori-probability assumption at the foundations of statistical mechanics is far too strong (since future conditioning reduces the class of allowed states). The test is based on a feature of this theory that was found necessary in order to recover standard (Born) probabilities in quantum measurements. Specifically, certain systems should have "noise" whose amplitude follows the long-tailed Cauchy distribution. This distribution is marked by the occasional occurrence of extremely large signals as well as a non-self-averaging property. The proposed test is a variant of the Stern-Gerlach experiment in which protocols are devised, some of which will require the presence of this noise, some of which will not. The likely observational schemes would involve the distinction between detection and non-detection of that "noise". The signal to be detected (or not) would be either single photons in the visible and UV range or electric fields (and related excitations) in the neighborhood of the ends of the magnets., Comment: This has already been published (see Journal reference), but I have since found an error and corrected it. See endnote 28

Using symmetric boundary conditions at separated times, I show analytically that both the time ordering of (macroscopic) causality and the direction of entropy increase follow from these boundary conditions. In particular, when the endpoints have low entropy, these arrows of time point away from the ends and toward the middle. Causality in this context means that when perturbations are applied, the effect of the perturbation---the macroscopic change in the system's behavior---is confined to one temporal side of the perturbations. These results hold for both mixing and integrable systems, although relaxation for integrable systems is incomplete. Simulations are presented for purposes of illustration., Comment: For the proceedings of the conference, "Time's Arrows, Quantum Measurements and Superluminal Behavior," Naples, Italy, October 2000. To be published by the Italian CNR. Contains two three-part figures

The second law of thermodynamics - the usual statement of the arrow of time - has been called the most fundamental law of physics. It is thus difficult to conceive that a single dynamical system could contain subsystems, in significant mutual contact, possessing opposite thermodynamic arrows of time. By examining cosmological justification for the usual arrow it is found that a consistent way to establish such justification is by giving symmetric boundary conditions at two (cosmologically remote) times and seeking directional behavior in between. Once this has been demonstrated, it is seen that entropy increase can be reversed and that the usual arrow is less totalitarian than previously believed. In the same vein, other boundary conditions, modeling shorter periods in the evolution of the cosmos, can be found that allow the simultaneous existence of two thermodynamic arrows, notwithstanding moderate interaction between the systems possessing those arrows. Physical consequences of the existence and detection of opposite-arrow regions are also considered., Comment: For the proceedings of the conference, Equations aux Derivees Partielles et Physique Mathematique, in honor of J. Vaillant, Paris, June 2000. B. Gaveau et al., editors

The extent to which a given wave function, $\psi$, is entangled is measured by minimizing the norm of $\psi$ minus all possible unentangled functions. This measure is given by the largest eigenvalue of $\psi^\dagger \psi$, considered as an operator. The definition is basis independent., Comment: 4 pages, plain TeX, no figures

Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which a unknown subgroup H of a group G must be determined from a quantum state ψ over G that is uniformly supported on a left coset of H. These hidden subgroup problems are typically solved by Fourier sampling: the quantum Fourier transform of ψ is computed and measured. When the underlying group is nonabelian, two important variants of the Fourier sampling paradigm have been identified: the weak standard method, where only representation names are measured, and the strong standard method, where full measurement (i.e., the row and column of the representation as well as its name) occurs. It has remained open whether the strong method is indeed stronger, that is, whether there are hidden subgroups that can be reconstructed via the strong method but not by the weak, or any other known, method.In this article, we settle this question in the affirmative. We show that hidden subgroups of semidirect products of the form ℤq × ℤp, where q | (p - 1) and q = p/polylog(p), can be efficiently determined by the strong standard method. Furthermore, the weak standard method and the "forgetful" abelian method are insufficient for these groups so that, in fact, it appears that use of the corresponding nonabelian representation theory is crucial. We extend this to an informationtheoretic solution for the hidden subgroup problem over the groups ℤq × ℤp where q | (p - 1) and, in particular, the affine groups Ap. Finally, we prove a simple closure property for the class of groups over which the hidden subgroup problem can be solved efficiently.

We show how the interplay of non-linear dynamics, self-gravity, and fluctuations leads to self-affine behavior of matter density correlations quite generically, i.e., with a power-law exponent whose value does not depend in a very direct way on the specific details of the dynamics. This we do by means of the Renormalization Group, a powerful analytic tool for extracting asymptotic behavior of many-body systems, Accepted for publication in Astronomy & Astrophysics. 10 pages using A&A style file; 2 eps figures