848 research outputs found
Efficient measurements, purification, and bounds on the mutual information
When a measurement is made on a quantum system in which classical information
is encoded, the measurement reduces the observers average Shannon entropy for
the encoding ensemble. This reduction, being the {\em mutual information}, is
always non-negative. For efficient measurements the state is also purified;
that is, on average, the observers von Neumann entropy for the state of the
system is also reduced by a non-negative amount. Here we point out that by
re-writing a bound derived by Hall [Phys. Rev. A {\bf 55}, 100 (1997)], which
is dual to the Holevo bound, one finds that for efficient measurements, the
mutual information is bounded by the reduction in the von Neumann entropy. We
also show that this result, which provides a physical interpretation for Hall's
bound, may be derived directly from the Schumacher-Westmoreland-Wootters
theorem [Phys. Rev. Lett. {\bf 76}, 3452 (1996)]. We discuss these bounds, and
their relationship to another bound, valid for efficient measurements on pure
state ensembles, which involves the subentropy.Comment: 4 pages, Revtex4. v3: rewritten and reinterpreted somewha
Exponents of quantum fixed-length pure state source coding
We derive the optimal exponent of the error probability of the quantum
fixed-length pure state source coding in both cases of blind coding and visible
coding. The optimal exponent is universally attained by Jozsa et al. (PRL, 81,
1714 (1998))'s universal code. In the direct part, a group representation
theoretical type method is essential. In the converse part, Nielsen and Kempe
(PRL, 86, 5184 (2001))'s lemma is essential.Comment: LaTeX2e and revetx4 with
aps,twocolumn,superscriptaddress,showpacs,pra,amssymb,amsmath. The previous
version has a mistak
The quantum dynamic capacity formula of a quantum channel
The dynamic capacity theorem characterizes the reliable communication rates
of a quantum channel when combined with the noiseless resources of classical
communication, quantum communication, and entanglement. In prior work, we
proved the converse part of this theorem by making contact with many previous
results in the quantum Shannon theory literature. In this work, we prove the
theorem with an "ab initio" approach, using only the most basic tools in the
quantum information theorist's toolkit: the Alicki-Fannes' inequality, the
chain rule for quantum mutual information, elementary properties of quantum
entropy, and the quantum data processing inequality. The result is a simplified
proof of the theorem that should be more accessible to those unfamiliar with
the quantum Shannon theory literature. We also demonstrate that the "quantum
dynamic capacity formula" characterizes the Pareto optimal trade-off surface
for the full dynamic capacity region. Additivity of this formula simplifies the
computation of the trade-off surface, and we prove that its additivity holds
for the quantum Hadamard channels and the quantum erasure channel. We then
determine exact expressions for and plot the dynamic capacity region of the
quantum dephasing channel, an example from the Hadamard class, and the quantum
erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections;
v3 has correction regarding the optimizatio
Reversible transformations from pure to mixed states, and the unique measure of information
Transformations from pure to mixed states are usually associated with
information loss and irreversibility. Here, a protocol is demonstrated allowing
one to make these transformations reversible. The pure states are diluted with
a random noise source. Using this protocol one can study optimal
transformations between states, and from this derive the unique measure of
information. This is compared to irreversible transformations where one does
not have access to noise. The ideas presented here shed some light on attempts
to understand entanglement manipulations and the inevitable irreversibility
encountered there where one finds that mixed states can contain "bound
entanglement".Comment: 10 pages, no figures, revtex4, table added, to appear in Phys. Rev.
Realization of quantum process tomography in NMR
Quantum process tomography is a procedure by which the unknown dynamical
evolution of an open quantum system can be fully experimentally characterized.
We demonstrate explicitly how this procedure can be implemented with a nuclear
magnetic resonance quantum computer. This allows us to measure the fidelity of
a controlled-not logic gate and to experimentally investigate the error model
for our computer. Based on the latter analysis, we test an important assumption
underlying nearly all models of quantum error correction, the independence of
errors on different qubits.Comment: 8 pages, 7 EPS figures, REVTe
Achievable rates for the Gaussian quantum channel
We study the properties of quantum stabilizer codes that embed a
finite-dimensional protected code space in an infinite-dimensional Hilbert
space. The stabilizer group of such a code is associated with a symplectically
integral lattice in the phase space of 2N canonical variables. From the
existence of symplectically integral lattices with suitable properties, we
infer a lower bound on the quantum capacity of the Gaussian quantum channel
that matches the one-shot coherent information optimized over Gaussian input
states.Comment: 12 pages, 4 eps figures, REVTe
An epitaxial model for heterogeneous nucleation on potent substrates
© The Minerals, Metals & Materials Society and ASM International 2012In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ÎT ). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h ), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h and ÎT ; h decreases; and ÎT increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.EPSRC Centre for Innovative Manufacturing in Liquid Metal Engineerin
Notes on entropic characteristics of quantum channels
One of most important issues in quantum information theory concerns
transmission of information through noisy quantum channels. We discuss few
channel characteristics expressed by means of generalized entropies. Such
characteristics can often be dealt in line with more usual treatment based on
the von Neumann entropies. For any channel, we show that the -average output
entropy of degree is bounded from above by the -entropy of the
input density matrix. Concavity properties of the -entropy exchange are
considered. Fano type quantum bounds on the -entropy exchange are
derived. We also give upper bounds on the map -entropies in terms of the
output entropy, corresponding to the completely mixed input.Comment: 10 pages, no figures. The statement of Proposition 1 is explicitly
illustrated with the depolarizing channel. The bibliography is extended and
updated. More explanations. To be published in Cent. Eur. J. Phy
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