2,780 research outputs found

### Characterization of Collective Gaussian Attacks and Security of Coherent-State Quantum Cryptography

We provide a simple description of the most general collective Gaussian
attack in continuous-variable quantum cryptography. In the scenario of such
general attacks, we analyze the asymptotic secret-key rates which are
achievable with coherent states, joint measurements of the quadratures and
one-way classical communication.Comment: 4 pages, 1 figure + 1 Table, REVteX. More descriptive titl

### Exponentially Enhanced Quantum Metrology

We show that when a suitable entanglement generating unitary operator
depending on a parameter is applied on N qubits in parallel, and an appropriate
observable is measured, a precision of order 2 raised to the power (-N) in
estimating the parameter may be achieved. This exponentially improves the
precision achievable in classical and in quantum non-entangling parallel
strategies. We propose a quantum-optics model of laser light interacting with
an N-qubit system, say a polyatomic molecule, via a generalized Jaynes-Cummings
interaction which, in principle, could achieve the exponentially enhanced
precision.Comment: 4 pages, 1 postscript figure ; typos correcte

### On Strong Superadditivity of the Entanglement of Formation

We employ a basic formalism from convex analysis to show a simple relation
between the entanglement of formation $E_F$ and the conjugate function $E^*$ of
the entanglement function E(\rho)=S(\trace_A\rho). We then consider the
conjectured strong superadditivity of the entanglement of formation $E_F(\rho)
\ge E_F(\rho_I)+E_F(\rho_{II})$, where $\rho_I$ and $\rho_{II}$ are the
reductions of $\rho$ to the different Hilbert space copies, and prove that it
is equivalent with subadditivity of $E^*$. As an application, we show that
strong superadditivity would follow from multiplicativity of the maximal
channel output purity for all non-trace-preserving quantum channels, when
purity is measured by Schatten $p$-norms for $p$ tending to 1.Comment: 11 pages; refs added, explanatory improvement

### Collaboration in Social Networks

The very notion of social network implies that linked individuals interact
repeatedly with each other. This allows them not only to learn successful
strategies and adapt to them, but also to condition their own behavior on the
behavior of others, in a strategic forward looking manner. Game theory of
repeated games shows that these circumstances are conducive to the emergence of
collaboration in simple games of two players. We investigate the extension of
this concept to the case where players are engaged in a local contribution game
and show that rationality and credibility of threats identify a class of Nash
equilibria -- that we call "collaborative equilibria" -- that have a precise
interpretation in terms of sub-graphs of the social network. For large network
games, the number of such equilibria is exponentially large in the number of
players. When incentives to defect are small, equilibria are supported by local
structures whereas when incentives exceed a threshold they acquire a non-local
nature, which requires a "critical mass" of more than a given fraction of the
players to collaborate. Therefore, when incentives are high, an individual
deviation typically causes the collapse of collaboration across the whole
system. At the same time, higher incentives to defect typically support
equilibria with a higher density of collaborators. The resulting picture
conforms with several results in sociology and in the experimental literature
on game theory, such as the prevalence of collaboration in denser groups and in
the structural hubs of sparse networks

### Multiple membrane cavity optomechanics

We investigate theoretically the extension of cavity optomechanics to
multiple membrane systems. We describe such a system in terms of the coupling
of the collective normal modes of the membrane array to the light fields. We
show these modes can be optically addressed individually and be cooled, trapped
and characterized, e.g. via quantum nondemolition measurements. Analogies
between this system and a linear chain of trapped ions or dipolar molecules
imply the possibility of related applications in the quantum regime.Comment: 4 pages, 2 figure

### Generalized uncertainty relations: Theory, examples, and Lorentz invariance

The quantum-mechanical framework in which observables are associated with
Hermitian operators is too narrow to discuss measurements of such important
physical quantities as elapsed time or harmonic-oscillator phase. We introduce
a broader framework that allows us to derive quantum-mechanical limits on the
precision to which a parameter---e.g., elapsed time---may be determined via
arbitrary data analysis of arbitrary measurements on $N$ identically prepared
quantum systems. The limits are expressed as generalized Mandelstam-Tamm
uncertainty relations, which involve the operator that generates displacements
of the parameter---e.g., the Hamiltonian operator in the case of elapsed time.
This approach avoids entirely the problem of associating a Hermitian operator
with the parameter. We illustrate the general formalism, first, with
nonrelativistic uncertainty relations for spatial displacement and momentum,
harmonic-oscillator phase and number of quanta, and time and energy and,
second, with Lorentz-invariant uncertainty relations involving the displacement
and Lorentz-rotation parameters of the Poincar\'e group.Comment: 39 pages of text plus one figure; text formatted in LaTe

### Optical implementation of continuous-variable quantum cloning machines

We propose an optical implementation of the Gaussian continuous-variable
quantum cloning machines. We construct a symmetric N -> M cloner which
optimally clones coherent states and we also provide an explicit design of an
asymmetric 1 -> 2 cloning machine. All proposed cloning devices can be built
from just a single non-degenerate optical parametric amplifier and several beam
splitters.Comment: 4 pages, 3 figures, REVTe

### Studies of the photoionization cross sections of CH_4

We present cross sections and asymmetry parameters for photoionization of the 1t_2 orbital of CH_4 using staticâexchange continuum orbitals of CH^+_4 to represent the photoelectron wave function. The calculations are done in the fixedânuclei approximation at a single internuclear geometry. To approximate the nearâthreshold behavior of these cross sections, we assumed that the photoelectron spectrum is a composite of three electronic bands associated with the JahnâTeller components of the distorted ion. The resulting cross sections reproduce the sharp rise seen at threshold in the experimental data and are in good agreement with experiment at higher energy. The agreement between the calculated and measured photoelectron asymmetry parameters is, however, less satisfactory

### Effect of Disorder Strength on Optimal Paths in Complex Networks

We study the transition between the strong and weak disorder regimes in the
scaling properties of the average optimal path $\ell_{\rm opt}$ in a disordered
Erd\H{o}s-R\'enyi (ER) random network and scale-free (SF) network. Each link
$i$ is associated with a weight $\tau_i\equiv\exp(a r_i)$, where $r_i$ is a
random number taken from a uniform distribution between 0 and 1 and the
parameter $a$ controls the strength of the disorder. We find that for any
finite $a$, there is a crossover network size $N^*(a)$ at which the transition
occurs. For $N \ll N^*(a)$ the scaling behavior of $\ell_{\rm opt}$ is in the
strong disorder regime, with $\ell_{\rm opt} \sim N^{1/3}$ for ER networks and
for SF networks with $\lambda \ge 4$, and $\ell_{\rm opt} \sim
N^{(\lambda-3)/(\lambda-1)}$ for SF networks with $3 < \lambda < 4$. For $N \gg
N^*(a)$ the scaling behavior is in the weak disorder regime, with $\ell_{\rm
opt}\sim\ln N$ for ER networks and SF networks with $\lambda > 3$. In order to
study the transition we propose a measure which indicates how close or far the
disordered network is from the limit of strong disorder. We propose a scaling
ansatz for this measure and demonstrate its validity. We proceed to derive the
scaling relation between $N^*(a)$ and $a$. We find that $N^*(a)\sim a^3$ for ER
networks and for SF networks with $\lambda\ge 4$, and $N^*(a)\sim
a^{(\lambda-1)/(\lambda-3)}$ for SF networks with $3 < \lambda < 4$.Comment: 6 pages, 6 figures. submitted to Phys. Rev.

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