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

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

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

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 static‐exchange continuum orbitals of CH^+_4 to represent the photoelectron wave function. The calculations are done in the fixed‐nuclei approximation at a single internuclear geometry. To approximate the near‐threshold behavior of these cross sections, we assumed that the photoelectron spectrum is a composite of three electronic bands associated with the Jahn–Teller 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.