655 research outputs found
Random quantum codes from Gaussian ensembles and an uncertainty relation
Using random Gaussian vectors and an information-uncertainty relation, we
give a proof that the coherent information is an achievable rate for
entanglement transmission through a noisy quantum channel. The codes are random
subspaces selected according to the Haar measure, but distorted as a function
of the sender's input density operator. Using large deviations techniques, we
show that classical data transmitted in either of two Fourier-conjugate bases
for the coding subspace can be decoded with low probability of error. A
recently discovered information-uncertainty relation then implies that the
quantum mutual information for entanglement encoded into the subspace and
transmitted through the channel will be high. The monogamy of quantum
correlations finally implies that the environment of the channel cannot be
significantly coupled to the entanglement, and concluding, which ensures the
existence of a decoding by the receiver.Comment: 9 pages, two-column style. This paper is a companion to
quant-ph/0702005 and quant-ph/070200
Entanglement in squeezed two-level atom
In the previous paper, we adopted the method using quantum mutual entropy to
measure the degree of entanglement in the time development of the
Jaynes-Cummings model. In this paper, we formulate the entanglement in the time
development of the Jaynes-Cummings model with squeezed states, and then show
that the entanglement can be controlled by means of squeezing.Comment: 6 pages, 5 figures, to be published in J.Phys.
Bounds on general entropy measures
We show how to determine the maximum and minimum possible values of one
measure of entropy for a given value of another measure of entropy. These
maximum and minimum values are obtained for two standard forms of probability
distribution (or quantum state) independent of the entropy measures, provided
the entropy measures satisfy a concavity/convexity relation. These results may
be applied to entropies for classical probability distributions, entropies of
mixed quantum states and measures of entanglement for pure states.Comment: 13 pages, 3 figures, published versio
Complementarity and the algebraic structure of 4-level quantum systems
The history of complementary observables and mutual unbiased bases is
reviewed. A characterization is given in terms of conditional entropy of
subalgebras. The concept of complementarity is extended to non-commutative
subalgebras. Complementary decompositions of a 4-level quantum system are
described and a characterization of the Bell basis is obtained.Comment: 19 page
Semiclassical properties and chaos degree for the quantum baker's map
We study the chaotic behaviour and the quantum-classical correspondence for
the baker's map. Correspondence between quantum and classical expectation
values is investigated and it is numerically shown that it is lost at the
logarithmic timescale. The quantum chaos degree is computed and it is
demonstrated that it describes the chaotic features of the model. The
correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy
Local asymptotic normality for qubit states
We consider n identically prepared qubits and study the asymptotic properties
of the joint state \rho^{\otimes n}. We show that for all individual states
\rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state
\rho^0, the joint state converges to a displaced thermal equilibrium state of a
quantum harmonic oscillator. The precise meaning of the convergence is that
there exist physical transformations T_{n} (trace preserving quantum channels)
which map the qubits states asymptotically close to their corresponding
oscillator state, uniformly over all states in the local neighborhood.
A few consequences of the main result are derived. We show that the optimal
joint measurement in the Bayesian set-up is also optimal within the pointwise
approach. Moreover, this measurement converges to the heterodyne measurement
which is the optimal joint measurement of position and momentum for the quantum
oscillator. A problem of local state discrimination is solved using local
asymptotic normality.Comment: 16 pages, 3 figures, published versio
Instruments and channels in quantum information theory
While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
typical inequalities for the quantum and classical relative entropies, many
bounds on the classical information extracted in a quantum measurement, of the
type of Holevo's bound, are obtained in a unified manner.Comment: 12 pages, revtex
A quantum measure of coherence and incompatibility
The well-known two-slit interference is understood as a special relation
between observable (localization at the slits) and state (being on both slits).
Relation between an observable and a quantum state is investigated in the
general case. It is assumed that the amount of ceherence equals that of
incompatibility between observable and state. On ground of this, an argument is
peresented that leads to a natural quantum measure of coherence, called
"coherence or incompatibility information". Its properties are studied in
detail making use of 'the mixing property of relative entropy' derived in this
article. A precise relation between the measure of coherence of an observable
and that of its coarsening is obtained and discussed from the intutitive point
of view. Convexity of the measure is proved, and thus the fact that it is an
information entity is established. A few more detailed properties of coherence
information are derived with a view to investigate final-state entanglement in
general repeatable measurement, and, more importantly, general bipartite
entanglement in follow ups of this study.Comment: 19 GS pages; supercedes quant-ph/030921
A note on the Landauer principle in quantum statistical mechanics
The Landauer principle asserts that the energy cost of erasure of one bit of
information by the action of a thermal reservoir in equilibrium at temperature
T is never less than . We discuss Landauer's principle for quantum
statistical models describing a finite level quantum system S coupled to an
infinitely extended thermal reservoir R. Using Araki's perturbation theory of
KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural
ergodicity assumption on the joint system S+R, that Landauer's bound saturates
for adiabatically switched interactions. The recent work of Reeb and Wolf on
the subject is discussed and compared
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