342 research outputs found
Information gain versus state disturbance for a single qubit
The trade-off between the information gain and the state disturbance is
derived for quantum operations on a single qubit prepared in a uniformly
distributed pure state. The derivation is valid for a class of measures
quantifying the state disturbance and the information gain which satisfy
certain invariance conditions. This class includes in particular the Shannon
entropy versus the operation fidelity. The central role in the derivation is
played by efficient quantum operations, which leave the system in a pure output
state for any measurement outcome. It is pointed out that the optimality of
efficient quantum operations among those inducing a given operator-valued
measure is related to Davies' characterization of convex invariant functions on
hermitian operators.Comment: 17 pages, LaTeX, osid.sty. Substantially expanded and generalize
Catalytic Staudinger-Vilarrasa Reaction for the Direct Ligation of Carboxylic Acids and Azides:Journal of Organic Chemistry
Integrability of Lie systems and some of its applications in physics
The geometric theory of Lie systems will be used to establish integrability
conditions for several systems of differential equations, in particular Riccati
equations and Ermakov systems. Many different integrability criteria in the
literature will be analyzed from this new perspective and some applications in
physics will be given.Comment: 16 page
Fidelity approach to quantum phase transitions
We review briefly the quantum fidelity approach to quantum phase transitions
in a pedagogical manner. We try to relate all established but scattered results
on the leading term of the fidelity into a systematic theoretical framework,
which might provide an alternative paradigm for understanding quantum critical
phenomena. The definition of the fidelity and the scaling behavior of its
leading term, as well as their explicit applications to the one-dimensional
transverse-field Ising model and the Lipkin-Meshkov-Glick model, are introduced
at the graduate-student level. In addition, we survey also other types of
fidelity approach, such as the fidelity per site, reduced fidelity,
thermal-state fidelity, operator fidelity, etc; as well as relevant works on
the fidelity approach to quantum phase transitions occurring in various
many-body systems.Comment: 41 pages, 31 figures. We apologize if we omit acknowledging your
relevant works. Do tell. An updated version with clearer figures can be found
at: http://www.phy.cuhk.edu.hk/~sjgu/fidelitynote.pd
Generating random density matrices
We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.Comment: 13 pages in latex with 8 figures include
Statistical distinguishability between unitary operations
The problem of distinguishing two unitary transformations, or quantum gates,
is analyzed and a function reflecting their statistical distinguishability is
found. Given two unitary operations, and , it is proved that there
always exists a finite number such that and are perfectly distinguishable, although they were not in the single-copy
case. This result can be extended to any finite set of unitary transformations.
Finally, a fidelity for one-qubit gates, which satisfies many useful properties
from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to
any finite set of gate
Multiphase progenetic development shaped the brain of flying archosaurs
The growing availability of virtual cranial endocasts of extinct and extant vertebrates has fueled the quest for endocranial characters that discriminate between phylogenetic groups and resolve their neural significances. We used geometric morphometrics to compare a phylogenetically and ecologically comprehensive data set of archosaurian endocasts along the deep evolutionary history of modern birds and found that this lineage experienced progressive elevation of encephalisation through several chapters of increased endocranial doming that we demonstrate to result from progenetic developments. Elevated encephalisation associated with progressive size reduction within Maniraptoriformes was secondarily exapted for flight by stem avialans. Within Mesozoic Avialae, endocranial doming increased in at least some Ornithurae, yet remained relatively modest in early Neornithes. During the Paleogene, volant non-neoavian birds retained ancestral levels of endocast doming where a broad neoavian niche diversification experienced heterochronic brain shape radiation, as did non-volant Palaeognathae. We infer comparable developments underlying the establishment of pterosaurian brain shapes
Monge Distance between Quantum States
We define a metric in the space of quantum states taking the Monge distance
between corresponding Husimi distributions (Q--functions). This quantity
fulfills the axioms of a metric and satisfies the following semiclassical
property: the distance between two coherent states is equal to the Euclidean
distance between corresponding points in the classical phase space. We compute
analytically distances between certain states (coherent, squeezed, Fock and
thermal) and discuss a scheme for numerical computation of Monge distance for
two arbitrary quantum states.Comment: 9 pages in LaTex - RevTex + 2 figures in ps. submitted to Phys. Rev.
Quantum correlations and distinguishability of quantum states
A survey of various concepts in quantum information is given, with a main
emphasis on the distinguishability of quantum states and quantum correlations.
Covered topics include generalized and least square measurements, state
discrimination, quantum relative entropies, the Bures distance on the set of
quantum states, the quantum Fisher information, the quantum Chernoff bound,
bipartite entanglement, the quantum discord, and geometrical measures of
quantum correlations. The article is intended both for physicists interested
not only by collections of results but also by the mathematical methods
justifying them, and for mathematicians looking for an up-to-date introductory
course on these subjects, which are mainly developed in the physics literature.Comment: Review article, 103 pages, to appear in J. Math. Phys. 55 (special
issue: non-equilibrium statistical mechanics, 2014
Markovian Master Equations: A Critical Study
We derive Markovian master equations of single and interacting harmonic
systems in different scenarios, including strong internal coupling. By
comparing the dynamics resulting from the corresponding Markovian master
equations with exact numerical simulations of the evolution of the global
system, we precisely delimit their validity regimes and assess the robustness
of the assumptions usually made in the process of deriving the reduced
dynamics. The proposed method is sufficiently general to suggest that the
conclusions made here are widely applicable to a large class of settings
involving interacting chains subject to a weak interaction with an environment.Comment: 40 pages, 14 figures, final versio
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