941 research outputs found
Landauer's erasure, error correction and entanglement
Classical and quantum error correction are presented in the form of Maxwell's
demon and their efficiency analyzed from the thermodynamic point of view. We
explain how Landauer's principle of information erasure applies to both cases.
By then extending this principle to entanglement manipulations we rederive
upper bounds on purification procedures thereby linking the ''no local increase
of entanglement'' principle to the Second Law of thermodynamics.Comment: 11 pages, 1 figure, to appear in The Proceedings of The Royal Societ
The Role of Relative Entropy in Quantum Information Theory
Quantum mechanics and information theory are among the most important
scientific discoveries of the last century. Although these two areas initially
developed separately it has emerged that they are in fact intimately related.
In this review I will show how quantum information theory extends traditional
information theory by exploring the limits imposed by quantum, rather than
classical mechanics on information storage and transmission. The derivation of
many key results uniquely differentiates this review from the "usual"
presentation in that they are shown to follow logically from one crucial
property of relative entropy. Within the review optimal bounds on the speed-up
that quantum computers can achieve over their classical counter-parts are
outlined using information theoretic arguments. In addition important
implications of quantum information theory to thermodynamics and quantum
measurement are intermittently discussed. A number of simple examples and
derivations including quantum super-dense coding, quantum teleportation,
Deutsch's and Grover's algorithms are also included.Comment: 40 pages, 11 figure
Entanglement in The Second Quantization Formalism
We study properties of entangled systems in the (mainly non-relativistic)
second quantization formalism. This is then applied to interacting and
non-interacting bosons and fermions and the differences between the two are
discussed. We present a general formalism to show how entanglement changes with
the change of modes of the system. This is illustrated with examples such as
the Bose condensation and the Unruh effect. It is then shown that a
non-interacting collection of fermions at zero temperature can be entangled in
spin providing that their distances do not exceed the inverse Fermi wavenumber.
Beyond this distance all bipartite entanglement vanishes, although classical
correlations still persist. We compute the entanglement of formation as well as
the mutual information for two spin-correlated electrons as a function of their
distance. The analogous non-interacting collection of bosons displays no
entanglement in the internal degrees of freedom. We show how to generalize our
analysis of the entanglement in the internal degrees of freedom to an arbitrary
number of particles.Comment: 11 pages, no figures, a few typos corrected and some references adde
Natural multiparticle entanglement in a Fermi gas
We investigate multipartite entanglement in a non-interacting fermion gas, as
a function of fermion separation, starting from the many particle fermion
density matrix. We prove that all multiparticle entanglement can be built only
out of two-fermion entanglement. Although from the Pauli exclusion principle we
would always expect entanglement to decrease with fermion distance, we
surprisingly find the opposite effect for certain fermion configurations. The
von Neumann entropy is found to be proportional to the volume for a large
number of particles even when they are arbitrarily close to each other. We will
illustrate our results using different configurations of two, three, and four
fermions at zero temperature although all our results can be applied to any
temperature and any number of particles.Comment: Replaced with revised editio
An Information--Theoretic Equality Implying the Jarzynski Relation
We derive a general information-theoretic equality for a system undergoing
two projective measurements separated by a general temporal evolution. The
equality implies the non-negativity of the mutual information between the
measurement outcomes of the earlier and later projective measurements. We show
that it also contains the Jarzynski relation between the average exponential of
the thermodynamical work and the exponential of the difference between the
initial and final free energy. Our result elucidates the information-theoretic
underpinning of thermodynamics and explains why the Jarzynski relation holds
identically both quantumly as well as classically.Comment: 2 pages, no figure
Foundations of Quantum Discord
This paper summarizes the basics of the notion of quantum discord and how it
relates to other types of correlations in quantum physics. We take the
fundamental information theoretic approach and illustrate our exposition with a
number of simple examples.Comment: 3 pages, special issue edited by Diogo de Oliveira Soares Pinto et a
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