2,234 research outputs found
Role of gravitational stress in land plant evolution - The gravitational factor in lignification Semiannual status report, period ending 31 Oct. 1968
Gravitational and mechanical stress effects on lignification in land plant
Identification of minimum phase preserving operators on the half line
Minimum phase functions are fundamental in a range of applications, including
control theory, communication theory and signal processing. A basic
mathematical challenge that arises in the context of geophysical imaging is to
understand the structure of linear operators preserving the class of minimum
phase functions. The heart of the matter is an inverse problem: to reconstruct
an unknown minimum phase preserving operator from its value on a limited set of
test functions. This entails, as a preliminary step, ascertaining sets of test
functions that determine the operator, as well as the derivation of a
corresponding reconstruction scheme. In the present paper we exploit a recent
breakthrough in the theory of stable polynomials to solve the stated inverse
problem completely. We prove that a minimum phase preserving operator on the
half line can be reconstructed from data consisting of its value on precisely
two test functions. And we derive an explicit integral representation of the
unknown operator in terms of this data. A remarkable corollary of the solution
is that if a linear minimum phase preserving operator has rank at least two,
then it is necessarily injective.Comment: 17 page
Experimental quantum key distribution over highly noisy channels
Error filtration is a method for encoding the quantum state of a single
particle into a higher dimensional Hilbert space in such a way that it becomes
less sensitive to phase noise. We experimentally demonstrate this method by
distributing a secret key over an optical fiber whose noise level otherwise
precludes secure quantum key distribution. By filtering out the phase noise, a
bit error rate of 15.3% +/- 0.1%, which is beyond the security limit, can be
reduced to 10.6% +/- 0.1%, thereby guaranteeing the cryptographic security.Comment: 4 pages, 2 figure
Economical quantum cloning in any dimension
The possibility of cloning a d-dimensional quantum system without an ancilla
is explored, extending on the economical phase-covariant cloning machine found
in [Phys. Rev. A {\bf 60}, 2764 (1999)] for qubits. We prove the impossibility
of constructing an economical version of the optimal universal cloning machine
in any dimension. We also show, using an ansatz on the generic form of cloning
machines, that the d-dimensional phase-covariant cloner, which optimally clones
all uniform superpositions, can be realized economically only in dimension d=2.
The used ansatz is supported by numerical evidence up to d=7. An economical
phase-covariant cloner can nevertheless be constructed for d>2, albeit with a
lower fidelity than that of the optimal cloner requiring an ancilla. Finally,
using again an ansatz on cloning machines, we show that an economical version
of the Fourier-covariant cloner, which optimally clones the computational basis
and its Fourier transform, is also possible only in dimension d=2.Comment: 8 pages RevTe
Reduced randomness in quantum cryptography with sequences of qubits encoded in the same basis
We consider the cloning of sequences of qubits prepared in the states used in
the BB84 or 6-state quantum cryptography protocol, and show that the
single-qubit fidelity is unaffected even if entire sequences of qubits are
prepared in the same basis. This result is of great importance for practical
quantum cryptosystems because it reduces the need for high-speed random number
generation without impairing on the security against finite-size attacks.Comment: 8 pages, submitted to PR
Extremal quantum cloning machines
We investigate the problem of cloning a set of states that is invariant under
the action of an irreducible group representation. We then characterize the
cloners that are "extremal" in the convex set of group covariant cloning
machines, among which one can restrict the search for optimal cloners. For a
set of states that is invariant under the discrete Weyl-Heisenberg group, we
show that all extremal cloners can be unitarily realized using the so-called
"double-Bell states", whence providing a general proof of the popular ansatz
used in the literature for finding optimal cloners in a variety of settings.
Our result can also be generalized to continuous-variable optimal cloning in
infinite dimensions, where the covariance group is the customary
Weyl-Heisenberg group of displacements.Comment: revised version accepted for publicatio
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