3,342 research outputs found
Inner structure of Gauss-Bonnet-Chern Theorem and the Morse theory
We define a new one form H^A based on the second fundamental tensor H^abA,
the Gauss-Bonnet-Chern form can be novelly expressed with this one-form. Using
the phi-mapping theory we find that the Gauss-Bonnet-Chern density can be
expressed in terms of the delta-function and the relationship between the
Gauss-Bonnet-Chern theorem and Hopf-Poincare theorem is given
straightforwardly. The topological current of the Gauss-Bonnet-Chern theorem
and its topological structure are discussed in details. At last, the Morse
theory formula of the Euler characteristic is generalized.Comment: 10 page
X-ray afterglow of GRB 050712: Multiple energy injections into the external shock
As indicated by the observed X-ray flares, a great amount of energy could be
intermediately released from the postburst central engine of gamma-ray bursts
(GRBs). As a natural consequence, the GRB external shock could be energized
over and over. With such a multiple energy injection model, we explore the
unique X-ray afterglow light curve of GRB 050712, which exists four apparent
shallow decay plateaus. Together with three early X-ray flares, the central
engine of GRB 050712 is supposed to release energy at least seven times after
the burst. Furthermore we find that the energy released during four plateaus
are all on the same order of magnitude, but the luminosity decreases with time
significantly. These results may provide some interesting implications for the
GRB central engine.Comment: 7 pages, two figures, Research in Astronomy and Astrophysics (RAA),
2014, in pres
Linearly-independent quantum states can be cloned
A fundamental question in quantum mechanics is, whether it is possible to
replicate an arbitrary unknown quantum state. Then famous quantum no-cloning
theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open
the following question: If the state is not arbitrary, but secretly chosen from
a certain set , whether is the
cloning possible? This question is of great practical significance because of
its applications in quantum information theory. If the states and are linearly-dependent, similar to the proof of
the no-cloning theorem, the linearity of quantum mechanics forbids such
replication. In this paper, we show that, if the states and are linearly-independent, they do can be cloned by a
unitary-reduction process.Comment: 9 pages, no figures, Late
Fault Tolerant Quantum Random Number Generator Certified by Majorana Fermions
Braiding of Majorana fermions gives accurate topological quantum operations
that are intrinsically robust to noise and imperfection, providing a natural
method to realize fault-tolerant quantum information processing. Unfortunately,
it is known that braiding of Majorana fermions is not sufficient for
implementation of universal quantum computation. Here we show that topological
manipulation of Majorana fermions provides the full set of operations required
to generate random numbers by way of quantum mechanics and to certify its
genuine randomness through violation of a multipartite Bell inequality. The
result opens a new perspective to apply Majorana fermions for robust generation
of certified random numbers, which has important applications in cryptography
and other related areas.Comment: 4pages of the main text+5 pages of supplementary informatio
Reply to the comment "quant-ph/9710002"
In the comment, Zanardi and Rasetti argue that several claims in our recent
letter (Phys. Rev. Lett. 79, 1953, 1997) are questionable. The reply shows
these claims remain true.Comment: 2 pages, Late
Decoherence of quantum registers
We consider decoherence of quantum registers, which consist of the qubits
sited approximately periodically in space. The sites of the qubits are
permitted to have a small random variance. We derive the explicit conditions
under which the qubits can be assumed decohering independently. In other
circumstances, the qubits are decohered cooperatively. We describe two kinds of
collective decoherence. In each case, a scheme is proposed for reducing the
collective decoherence. The schemes operate by encoding the input states of the
qubits into some ''subdecoherent'' states.Comment: 12 pages, no figures, Late
Certification of Boson Sampling Devices with Coarse-Grained Measurements
A boson sampling device could efficiently sample from the output probability
distribution of noninteracting bosons undergoing many-body interference. This
problem is not only classically intractable, but its solution is also believed
to be classically unverifiable. Hence, a major difficulty in experiment is to
ensure a boson sampling device performs correctly. We present an experimental
friendly scheme to extract useful and robust information from the quantum boson
samplers based on coarse-grained measurements. The procedure can be applied to
certify the equivalence of boson sampling devices while ruling out alternative
fraudulent devices. We perform numerical simulations to demonstrate the
feasibility of the method and consider the effects of realistic noise. Our
approach is expected to be generally applicable to other many-body
certification tasks beyond the boson sampling problem.Comment: 8 pages including Supplemental Materials, 7 figures, 3 table
Two non-orthogonal states can be cloned by a unitary-reduction process
We show that, there are physical means for cloning two non-orthogonal pure
states which are secretly chosen from a certain set % \$={ | \Psi_0 > , |
\Psi_1 > }. The states are cloned through a unitary evolution together with a
measurement. The cloning efficiency can not attain 100%. With some negative
measurement results, the cloning fails.Comment: 9 pages, no figures, Late
Reducing spatially correlated noise and decoherence with quantum error correcting codes
It is shown that the noise process in quantum computation can be described by
spatially correlated decoherence and dissipation. We demonstrate that the
conventional quantum error correcting codes correcting for single-qubit errors
are applicable for reducing spatially correlated noise.Comment: 8 pages, late
Pulse controlled noise suppressed quantum computation
To make arbitrarily accurate quantum computation possible, practical
realization of quantum computers will require suppressing noise in quantum
memory and gate operations to make it below a threshold value. A scheme based
on realistic quantum computer models is described for suppressing noise in
quantum computation without the cost of stringent quantum computing resources.Comment: 12 pages, late
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