382 research outputs found
Codes and noncommutative stochastic matrices
Given a matrix over a skew field fixing the column t (1,...,1), we give formulas for a row vector fixed by this matrix. The same techniques are applied to give noncommutative extensions of probabilistic properties of codes
On classical and quantum liftings
We analyze the procedure of lifting in classical stochastic and quantum
systems. It enables one to `lift' a state of a system into a state of
`system+reservoir'. This procedure is important both in quantum information
theory and the theory of open systems. We illustrate the general theory of
liftings by a particular class related to so called circulant states.Comment: 25 page
Optimality in Quantum Data Compression using Dynamical Entropy
In this article we study lossless compression of strings of pure quantum
states of indeterminate-length quantum codes which were introduced by
Schumacher and Westmoreland. Past work has assumed that the strings of quantum
data are prepared to be encoded in an independent and identically distributed
way. We introduce the notion of quantum stochastic ensembles, allowing us to
consider strings of quantum states prepared in a more general way. For any
identically distributed quantum stochastic ensemble we define an associated
quantum Markov chain and prove that the optimal average codeword length via
lossless coding is equal to the quantum dynamical entropy of the associated
quantum Markov chain
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page
Multifractals, Mumford curves, and Eternal Inflation
We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and
Susskind to constructions of stochastic processes arising from quantum
statistical mechanical systems on Cuntz--Krieger algebras. We extend the
eternal inflation model from the Bruhat--Tits tree to quotients by p-adic
Schottky groups, again using quantum statistical mechanics on graph algebras.Comment: 19 pages, LaTeX, 4 pdf figure
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