14 research outputs found
Quantum Data Compression and Relative Entropy Revisited
B. Schumacher and M. Westmoreland have established a quantum analog of a
well-known classical information theory result on a role of relative entropy as
a measure of non-optimality in (classical) data compression. In this paper, we
provide an alternative, simple and constructive proof of this result by
constructing quantum compression codes (schemes) from classical data
compression codes. Moreover, as the quantum data compression/coding task can be
effectively reduced to a (quasi-)classical one, we show that relevant results
from classical information theory and data compression become applicable and
therefore can be extended to the quantum domain.Comment: 7 pages, no figures, minor revisio
Typical support and Sanov large deviations of correlated states
Discrete stationary classical processes as well as quantum lattice states are
asymptotically confined to their respective typical support, the exponential
growth rate of which is given by the (maximal ergodic) entropy. In the iid case
the distinguishability of typical supports can be asymptotically specified by
means of the relative entropy, according to Sanov's theorem. We give an
extension to the correlated case, referring to the newly introduced class of
HP-states.Comment: 29 pages, no figures, references adde
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and Kolmogorov complexity per
symbol are related by a theorem of Brudno. In this paper, we prove a quantum
version of this theorem, connecting the von Neumann entropy rate and two
notions of quantum Kolmogorov complexity, both based on the shortest qubit
descriptions of qubit strings that, run by a universal quantum Turing machine,
reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in
the Communications in Mathematical Physics
(http://www.springerlink.com/content/1432-0916/
Artificial Sequences and Complexity Measures
In this paper we exploit concepts of information theory to address the
fundamental problem of identifying and defining the most suitable tools to
extract, in a automatic and agnostic way, information from a generic string of
characters. We introduce in particular a class of methods which use in a
crucial way data compression techniques in order to define a measure of
remoteness and distance between pairs of sequences of characters (e.g. texts)
based on their relative information content. We also discuss in detail how
specific features of data compression techniques could be used to introduce the
notion of dictionary of a given sequence and of Artificial Text and we show how
these new tools can be used for information extraction purposes. We point out
the versatility and generality of our method that applies to any kind of
corpora of character strings independently of the type of coding behind them.
We consider as a case study linguistic motivated problems and we present
results for automatic language recognition, authorship attribution and self
consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression
approach to Information Extraction and Classification" by A. Baronchelli and
V. Loreto. 15 pages; 5 figure
Improved Algorithmic Cooling for Scalable NMR Quantum Computers
The scaling of NMR ensemble computers is currently one of the main obstacles to building larger-scale quantum computing devices. To achieve scalability, one needs a large number of highly polarized spins in liquid nuclearspin systems at finite temperature. In quantum computing terminology, such spin-half states are (almost) pure qubit states. Producing highly polarized spins (almost pure qubit states) out of non-polarized spins (non-pure qubit states) is sometimes called ”purification ”. From a thermodynamic point of view, purification can be viewed as cooling spins to a very low temperature. In this preliminary work, we study the optimality of purification as a tradeoff between the number of cooled spins and the closeness of their quantum state to the ideal pure state