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A \textit{grounded set family} on $I$ is a subset $\mathcal{F}\subseteq2^I$ such that $\emptyset\in\mathcal{F}$. We study a linearized Hopf monoid \textbf{SF} on grounded set families, with restriction and contraction inspired by the corresponding operations for antimatroids. Many known combinatorial species, including simplicial complexes and matroids, form Hopf submonoids of \textbf{SF}, although not always with the "standard" Hopf structure (for example, our contraction operation is not the usual contraction of matroids). We use the topological methods of Aguiar and Ardila to obtain a cancellation-free antipode formula for the Hopf submonoid of lattices of order ideals of finite posets. Furthermore, we prove that the Hopf algebra of lattices of order ideals of chain gangs extends the Hopf algebra of symmetric functions, and that its character group extends the group of formal power series in one variable with constant term 1 under multiplication., Comment: 22 pages

Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counter-intuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialisation, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode, and the logical basis can be deterministically initialised from thermal equilibrium. All logical operations of this encoding can be performed with continuous-variable interaction and measurement only. Without the necessity of ground state cooling, our proposal could broaden the set of candidate systems for implementing quantum computers, and reduce the reliance on demanding refrigerating facility for current quantum computing architectures. Additionally, our protocol can enhance the noise tolerance of logical qubit even if the system can be efficiently cooled., Comment: Updated references, close to published version

We analyze an experimental method for creating interesting nonclassical states by processing the entanglement generated when two large coherent states interact in a cross-Kerr medium. We specifically investigate the effects of loss and noise in every mode of the experiment, as well as the effect of "binning" the post-selection outcomes. Even with these imperfections, we find an optimal set of currently-achievable parameters which would allow a proof-of-principle demonstration of number squeezing in states with large mean photon number. We discuss other useful states which can be generated with the same experimental tools, including a class of states which contain coherent superpositions of differing photon numbers, e.g. good approximations to the state $\frac{1}{\sqrt{2}} (|0\rangle+|20\rangle)$. Finally, we suggest one possible application of this state in the field of optomechanics., Comment: 8 pages, 7 figures

We propose a method to manipulate the normal modes in a chain of trapped ions using only two lasers. Linear chains of trapped ions have proven experimentally to be highly controllable quantum systems with a variety of refined techniques for preparation, evolution, and readout, however, typically for quantum information processing applications people have been interested in using the internal levels of the ions as the computational basis. We analyse the case where the motional degrees of freedom of the ions is the quantum system of interest, and where the internal levels are leveraged to facilitate interactions. In particular, we focus on an analysis of mode-mixing of phonons in different normal modes to mimic the quantum optical equivalent of a beam splitter.

The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum solution that achieves the unconditional security of a user's privacy using the practical technology of continuous variables. We demonstrate losses of up to 10 km both ways between the client and the server and show that security can still be achieved. Our approach offers a number of practical benefits, which can ultimately allow for the potential widespread adoption of this quantum technology in future cloud-based computing networks., Comment: Main text (6 pages) plus Appendices (14 pages), 13 figures

We propose a method to improve the performance of two entanglement-based continuous-variable quantum key distribution protocols using noiseless linear amplifiers. The two entanglement-based schemes consist of an entanglement distribution protocol with an untrusted source and an entanglement swapping protocol with an untrusted relay. Simulation results show that the noiseless linear amplifiers can improve the performance of these two protocols, in terms of maximal transmission distances, when we consider small amounts of entanglement, as typical in realistic setups., Comment: Special issue on Quantum Cryptography

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has led to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on cluster states that is feasible with today's technology., Comment: 7 pages, 1 figure

We show how weak non-linearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schr\"odinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that over any distance in this channel the quantum bit error rate is identically zero, in principle, and the states in the protocol are always able to violate a Bell inequality. The protocol is found to be superior in some regimes to a device-independent QKD protocol based on polarization entangled states in a depolarizing channel. Finally, we propose an implementation for the optimal filters and measurements., Comment: Comments welcome

In order to achieve universal quantum computation using continuous variables, one needs to jump out of the set of Gaussian operations and have a non-Gaussian element, such as the cubic phase gate. However, such a gate is currently very difficult to implement in practice. Here we introduce an experimentally viable 'repeat-until-success' approach to generating the cubic phase gate, which is achieved using sequential photon subtractions and Gaussian operations. We find that our scheme offers benefits in terms of the expected time until success, although we require a primitive quantum memory., Comment: 7 pages, 4 figures

We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable device-independent quantum key distribution to this encoding enables a continuous-variable analogue. Since the security of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find that our protocol is valid over the same distances as its discrete-variable counterpart, except that we are able to take advantage of high efficiency commercially available detectors where, for the most part, only homodyne detection is required. This offers the potential of removing the difficulty in closing the loopholes associated with Bell inequalities., Comment: 6 pages, 1 figure

The need for high fidelity quantum teleportation arises in a variety of quantum algorithms and protocols. Unfortunately, conventional continuous variable teleportation schemes rely on EPR states that yield a fidelity that approaches unity only in the limit of an unphysical amount of squeezing. A new method, which utilizes an ensemble of single photon entangled states to teleport continuous variable states with fidelity approaching unity with finite resources was recently proposed by Andersen and Ralph [Phys. Rev. Lett. 111, 050504 (2013)]. We extend these ideas to consider the general case of using maximally entangled states of an arbitrary dimension to teleport a continuous variable state and discuss how the corresponding results are affected.

We present analysis of both the short-term optical and long-term multiwavelength variability of CTA 102. In 2004, this object was observed in an intense optical flaring state. Extensive R-band microvariability observations were carried out during this high state. In 2005, we obtained several weeks of contemporaneous radio, optical, and X-ray observations of CTA 102. These observations recorded distinct flaring activity in all three wavebands. Subsequent analysis revealed that this object may appear redder when in a brighter optical state, and that the X-ray, optical, and radio activity do not appear to be correlated. The shape of the observed spectral energy distributions suggests that both synchrotron-related and external inverse Compton processes may contribute to the X-ray emission. Our results are also compared with other results on this object and archival microvariability observations. It appears that more rapid, dramatic microvariability events occur when CTA 102 is in an elevated optical flux state., Comment: AJ in press. Manuscript contains 29 pages, 13 figures

We present the results of extensive multi-frequency monitoring of the radio galaxy 3C 120 between 2002 and 2007 at X-ray, optical, and radio wave bands, as well as imaging with the Very Long Baseline Array (VLBA). Over the 5 yr of observation, significant dips in the X-ray light curve are followed by ejections of bright superluminal knots in the VLBA images. Consistent with this, the X-ray flux and 37 GHz flux are anti-correlated with X-ray leading the radio variations. This implies that, in this radio galaxy, the radiative state of accretion disk plus corona system, where the X-rays are produced, has a direct effect on the events in the jet, where the radio emission originates. The X-ray power spectral density of 3C 120 shows a break, with steeper slope at shorter timescale and the break timescale is commensurate with the mass of the central black hole based on observations of Seyfert galaxies and black hole X-ray binaries. These findings provide support for the paradigm that black hole X-ray binaries and active galactic nuclei are fundamentally similar systems, with characteristic time and size scales linearly proportional to the mass of the central black hole. The X-ray and optical variations are strongly correlated in 3C 120, which implies that the optical emission in this object arises from the same general region as the X-rays, i.e., in the accretion disk-corona system. We numerically model multi-wavelength light curves of 3C 120 from such a system with the optical-UV emission produced in the disk and the X-rays generated by scattering of thermal photons by hot electrons in the corona. From the comparison of the temporal properties of the model light curves to that of the observed variability, we constrain the physical size of the corona and the distances of the emitting regions from the central BH., Comment: Accepted for publication in the Astrophysical Journal. 28 pages, 21 figures, 2 tables

We present results from a multi-year monitoring campaign of the broad-line radio galaxy 3C 120, using the Rossi X-ray Timing Explorer (RXTE) for nearly five years of observations. Additionally, we present coincident optical monitoring using data from several ground-based observatories. Both the X-ray and optical emission are highly variable and appear to be strongly correlated, with the X-ray emission leading the optical by 28 days. The X-ray power density spectrum is best fit by a broken power law, with a low-frequency slope of -1.2, breaking to a high-frequency slope of -2.1, and a break frequency of log nu_b=-5.75 Hz, or 6.5 days. This value agrees well with the value expected based on 3C 120's mass and accretion rate. We find no evidence for a second break in the power spectrum. Combined with a moderately soft X-ray spectrum (Gamma=1.8) and a moderately high accretion rate (mdot / mdot_Edd ~ 0.3), this indicates that 3C 120 fits in wellwith the high/soft variability state found in most other AGNs. Previous studies have shown that the spectrum has a strong Fe K-alpha line, which may be relativistically broadened. The presence of this line, combined with a power spectrum similar to that seen in Seyfert galaxies, suggests that the majority of the X-ray emission in this object arises in or near the disk, and not in the jet., Comment: 19 pages, 6 figures. Accepted for publication in ApJ

The TeV blazar PKS 2155--304 was the subject of an intensive 2 week optical and near-infrared observing campaign in 2004 August with the CTIO 0.9m telescope. During this time, simultaneous X-ray data from RXTE were also obtained. We compare the results of our observations to the results from two previous simultaneous multiwavelength campaigns on PKS 2155-304. We conclude that the correlation between the X-ray and UV/optical variability is strongest and the time lag is shortest (only a few hours) when the object is brightest. As the object becomes fainter, the correlations are weaker and the lags longer, increasing to a few days. Based on the results of four campaigns, we find evidence for a linear relationship between the mean optical brightness and lag time of X-ray and UV/optical events. Furthermore, we assert that this behavior, along with the different multiwavelength flare lag times across different flux states is consistent with a highly relativistic shock propagating down the jet producing the flares observed during a high state. In a quiescent state, the variability is likely to be due to a number of factors including both the jet and contributions outside of the jet, such as the accretion disk., Comment: 23 pages, 8 figures, to be published in the Astrophysical Journal, volume 671

We present results of a 3 year monitoring campaign of the Seyfert 1 galaxy Markarian 509, using X-ray data from the Rossi X-ray Timing Explorer (RXTE) and optical data taken by the SMARTS consortium. Both light curves show significant variations, and are strongly correlated with the optical flux leading the X-ray flux by 15 days. The X-ray power spectrum shows a steep high-frequency slope of -2.0, breaking to a slope of -1.0 at at timescale of 34 days. The lag from optical to X-ray emission is most likely caused by variations in the accretion disk propagating inward., Comment: 13 pages, 3 figures. Accepted for publication in the Astrophysical Journal

PG 1553+11 was the target of a coordinated three week multiwavelength campaign during 2003 April and May. A significant X-ray flare was observed during the second half of this campaign. Although no optical flare was recorded during the X-ray campaign, optical observations obtained immediately prior to the campaign displayed a higher flux than that recorded during the campaign. An optical flare was observed a few days after the end of the X-ray campaign and may be related to the X-ray flare. Radio observations were made at three frequencies, with no significant changes in flux detected near the times of the optical and X-ray flares. The spectral energy distributions and flux ratios in different wavebands observed for this object are compared to other X-ray selected blazars to demonstrate how PG 1553+11 is an extreme member of this group., Comment: 28 pages, 4 figures, 7 tables. Accepted for publication in AJ