3,323 research outputs found
Quantum entanglement
All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory}. But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy.
This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding. However, it appeared that this new resource is
very complex and difficult to detect. Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure.
This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying. In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations. They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon. A basic role of entanglement
witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended)
presentation, updated references, minor changes, submitted to Rev. Mod. Phys
The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory
The present paper is both a review on the Feynman problem, and an original
research presentation on the relations between Fermionic theories and qubits
theories, both regarded in the novel framework of operational probabilistic
theories. The most relevant results about the Feynman problem of simulating
Fermions with qubits are reviewed, and in the light of the new original results
the problem is solved. The answer is twofold. On the computational side the two
theories are equivalent, as shown by Bravyi and Kitaev (Ann. Phys. 298.1
(2002): 210-226). On the operational side the quantum theory of qubits and the
quantum theory of Fermions are different, mostly in the notion of locality,
with striking consequences on entanglement. Thus the emulation does not respect
locality, as it was suspected by Feynman (Int. J. Theor. Phys. 21.6 (1982):
467-488).Comment: 46 pages, review about the "Feynman problem". Fixed many typo
Large-scale simultaneous inference under dependence
Simultaneous, post-hoc inference is desirable in large-scale hypotheses
testing as it allows for exploration of data while deciding on criteria for
proclaiming discoveries. It was recently proved that all admissible post-hoc
inference methods for the number of true discoveries must be based on closed
testing. In this paper we investigate tractable and efficient closed testing
with local tests of different properties, such as monotonicty, symmetry and
separability, meaning that the test thresholds a monotonic or symmetric
function or a function of sums of test scores for the individual hypotheses.
This class includes well-known global null tests by Fisher, Stouffer and
Ruschendorf, as well as newly proposed ones based on harmonic means and Cauchy
combinations. Under monotonicity, we propose a new linear time statistic
("coma") that quantifies the cost of multiplicity adjustments. If the tests are
also symmetric and separable, we develop several fast (mostly linear-time)
algorithms for post-hoc inference, making closed testing tractable. Paired with
recent advances in global null tests based on generalized means, our work
immediately instantiates a series of simultaneous inference methods that can
handle many complex dependence structures and signal compositions. We provide
guidance on choosing from these methods via theoretical investigation of the
conservativeness and sensitivity for different local tests, as well as
simulations that find analogous behavior for local tests and full closed
testing. One result of independent interest is the following: if
are -values from a multivariate Gaussian with arbitrary
covariance, then their arithmetic average P satisfies for
.Comment: 40 page
Isogenies of Elliptic Curves: A Computational Approach
Isogenies, the mappings of elliptic curves, have become a useful tool in
cryptology. These mathematical objects have been proposed for use in computing
pairings, constructing hash functions and random number generators, and
analyzing the reducibility of the elliptic curve discrete logarithm problem.
With such diverse uses, understanding these objects is important for anyone
interested in the field of elliptic curve cryptography. This paper, targeted at
an audience with a knowledge of the basic theory of elliptic curves, provides
an introduction to the necessary theoretical background for understanding what
isogenies are and their basic properties. This theoretical background is used
to explain some of the basic computational tasks associated with isogenies.
Herein, algorithms for computing isogenies are collected and presented with
proofs of correctness and complexity analyses. As opposed to the complex
analytic approach provided in most texts on the subject, the proofs in this
paper are primarily algebraic in nature. This provides alternate explanations
that some with a more concrete or computational bias may find more clear.Comment: Submitted as a Masters Thesis in the Mathematics department of the
University of Washingto
The quantum structure of spacetime at the Planck scale and quantum fields
We propose uncertainty relations for the different coordinates of spacetime
events, motivated by Heisenberg's principle and by Einstein's theory of
classical gravity. A model of Quantum Spacetime is then discussed where the
commutation relations exactly implement our uncertainty relations.
We outline the definition of free fields and interactions over QST and take
the first steps to adapting the usual perturbation theory. The quantum nature
of the underlying spacetime replaces a local interaction by a specific nonlocal
effective interaction in the ordinary Minkowski space. A detailed study of
interacting QFT and of the smoothing of ultraviolet divergences is deferred to
a subsequent paper.
In the classical limit where the Planck length goes to zero, our Quantum
Spacetime reduces to the ordinary Minkowski space times a two component space
whose components are homeomorphic to the tangent bundle TS^2 of the 2-sphere.
The relations with Connes' theory of the standard model will be studied
elsewhere.Comment: TeX, 37 pages. Since recent and forthcoming articles (hep-th/0105251,
hep-th/0201222, hep-th/0301100) are based on this paper, we thought it would
be convenient for the readers to have it available on the we
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