Time reversed encryption

Time reversal frameness and superselection

Authors: Gilad Gour, Barry C. Sanders, Peter S. Turner
(Submitted on 24 Nov 2008)
Abstract: We show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time-reversal superselection so that two parties lacking knowledge about the other's direction of time can still communicate. We identify the time-reversal reference frame resource states and determine the corresponding frameness monotone, which connects time-reversal frameness to entanglement. In contradistinction to other studies of reference frame quantum resources, this is the first analysis that involves an antiunitary rather than unitary representation.

Mining the Primes

The first digit frequencies of primes and Riemann zeta zeros tend to uniformity following a size-dependent generalized Benford's law

Authors: Bartolo Luque, Lucas Lacasa

(Submitted on 20 Nov 2008)

Abstract: Prime numbers seem to distribute among the natural numbers with no other law than that of chance, however its global distribution presents a quite remarkable smoothness. Such interplay between randomness and regularity has motivated scientists of all ages to search for local and global patterns in this distribution that eventually could shed light into the ultimate nature of primes. In this work we show that a generalization of the well known first-digit Benford's law, which addresses the rate of appearance of a given leading digit d in data sets, describes with astonishing precision the statistical distribution of leading digits in the prime numbers sequence. Moreover, a reciprocal version of this pattern also takes place in the sequence of the nontrivial Riemann zeta zeros. We prove that the prime number theorem is, in the last analysis, the responsible of these patterns. Some new relations concerning the prime numbers distribution are also deduced, including a new approximation to the counting function pi(n). Furthermore, some relations concerning the statistical conformance to this generalized Benford's law are derived. Some applications are finally discussed.