1,520 research outputs found
Finite size scaling in three-dimensional bootstrap percolation
We consider the problem of bootstrap percolation on a three dimensional
lattice and we study its finite size scaling behavior. Bootstrap percolation is
an example of Cellular Automata defined on the -dimensional lattice
in which each site can be empty or occupied by a single
particle; in the starting configuration each site is occupied with probability
, occupied sites remain occupied for ever, while empty sites are occupied by
a particle if at least among their nearest neighbor sites are
occupied. When is fixed, the most interesting case is the one :
this is a sort of threshold, in the sense that the critical probability
for the dynamics on the infinite lattice switches from zero to one
when this limit is crossed. Finite size effects in the three-dimensional case
are already known in the cases : in this paper we discuss the case
and we show that the finite size scaling function for this problem is
of the form . We prove a conjecture proposed by
A.C.D. van Enter.Comment: 18 pages, LaTeX file, no figur
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
Internal dissipation of a polymer
The dynamics of flexible polymer molecules are often assumed to be governed
by hydrodynamics of the solvent. However there is considerable evidence that
internal dissipation of a polymer contributes as well. Here we investigate the
dynamics of a single chain in the absence of solvent to characterize the nature
of this internal friction. We model the chains as freely hinged but with
localized bond angles and 3-fold symmetric dihedral angles. We show that the
damping is close but not identical to Kelvin damping, which depends on the
first temporal and second spatial derivative of monomer position. With no
internal potential between monomers, the magnitude of the damping is small for
long wavelengths and weakly damped oscillatory time dependent behavior is seen
for a large range of spatial modes. When the size of the internal potential is
increased, such oscillations persist, but the damping becomes larger. However
underdamped motion is present even with quite strong dihedral barriers for long
enough wavelengths.Comment: 6 pages, 8 figure
Multipartite Asymmetric Quantum Cloning
We investigate the optimal distribution of quantum information over
multipartite systems in asymmetric settings. We introduce cloning
transformations that take identical replicas of a pure state in any
dimension as input, and yield a collection of clones with non-identical
fidelities. As an example, if the clones are partitioned into a set of
clones with fidelity and another set of clones with fidelity ,
the trade-off between these fidelities is analyzed, and particular cases of
optimal cloning machines are exhibited. We also present an
optimal cloning machine, which is the first known example of a
tripartite fully asymmetric cloner. Finally, it is shown how these cloning
machines can be optically realized.Comment: 5 pages, 2 figure
Reduction criterion for separability
We introduce a separability criterion based on the positive map Î:Ďâ(Tr Ď)-Ď, where Ď is a trace-class Hermitian operator. Any separable state is mapped by the tensor product of Î and the identity into a non-negative operator, which provides a simple necessary condition for separability. This condition is generally not sufficient because it is vulnerable to the dilution of entanglement. In the special case where one subsystem is a quantum bit, Î reduces to time reversal, so that this separability condition is equivalent to partial transposition. It is therefore also sufficient for 2Ă2 and 2Ă3 systems. Finally, a simple connection between this map for two qubits and complex conjugation in the âmagicâ basis [Phys. Rev. Lett. 78, 5022 (1997)] is displayed
Cloning the entanglement of a pair of quantum bits
It is shown that any quantum operation that perfectly clones the entanglement
of all maximally-entangled qubit pairs cannot preserve separability. This
``entanglement no-cloning'' principle naturally suggests that some approximate
cloning of entanglement is nevertheless allowed by quantum mechanics. We
investigate a separability-preserving optimal cloning machine that duplicates
all maximally-entangled states of two qubits, resulting in 0.285 bits of
entanglement per clone, while a local cloning machine only yields 0.060 bits of
entanglement per clone.Comment: 4 pages Revtex, 2 encapsulated Postscript figures, one added autho
Quantum conditional operator and a criterion for separability
We analyze the properties of the conditional amplitude operator, the quantum
analog of the conditional probability which has been introduced in
[quant-ph/9512022]. The spectrum of the conditional operator characterizing a
quantum bipartite system is invariant under local unitary transformations and
reflects its inseparability. More specifically, it is shown that the
conditional amplitude operator of a separable state cannot have an eigenvalue
exceeding 1, which results in a necessary condition for separability. This
leads us to consider a related separability criterion based on the positive map
, where is an Hermitian operator. Any
separable state is mapped by the tensor product of this map and the identity
into a non-negative operator, which provides a simple necessary condition for
separability. In the special case where one subsystem is a quantum bit,
reduces to time-reversal, so that this separability condition is
equivalent to partial transposition. It is therefore also sufficient for
and systems. Finally, a simple connection between this
map and complex conjugation in the "magic" basis is displayed.Comment: 19 pages, RevTe
Quantum Cloning of Mixed States in Symmetric Subspace
Quantum cloning machine for arbitrary mixed states in symmetric subspace is
proposed. This quantum cloning machine can be used to copy part of the output
state of another quantum cloning machine and is useful in quantum computation
and quantum information. The shrinking factor of this quantum cloning achieves
the well-known upper bound. When the input is identical pure states, two
different fidelities of this cloning machine are optimal.Comment: Revtex, 4 page
Phase-Conjugated Inputs Quantum Cloning Machines
A quantum cloning machine is introduced that yields identical optimal
clones from replicas of a coherent state and replicas of its phase
conjugate. It also optimally produces phase-conjugated clones at no
cost. For well chosen input asymmetries , this machine is shown to
provide better cloning fidelities than the standard cloner. The
special cases of the optimal balanced cloner () and the optimal
measurement () are investigated.Comment: 4 pages (RevTex), 2 figure
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