Experimental estimation of the dimension of classical and quantum systems

An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness answers this question, as it allows one to bound the dimension of an unknown classical or quantum system in a device-independent manner, that is, only from the statistics of measurements performed on it. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario. We use pairs of photons entangled in both polarization and orbital angular momentum to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our results open new avenues for the device-independent estimation of unknown quantum systems and for applications in quantum information science.Comment: See also similar, independent and jointly submitted work of J. Ahrens et al., quant-ph/1111.127

On Quantum Advantage in Information Theoretic Single-Server PIR

In (single-server) Private Information Retrieval (PIR), a server holds a large database $DB$ of size $n$, and a client holds an index $i \in [n]$ and wishes to retrieve $DB[i]$ without revealing $i$ to the server. It is well known that information theoretic privacy even against an `honest but curious' server requires $\Omega(n)$ communication complexity. This is true even if quantum communication is allowed and is due to the ability of such an adversarial server to execute the protocol on a superposition of databases instead of on a specific database (`input purification attack'). Nevertheless, there have been some proposals of protocols that achieve sub-linear communication and appear to provide some notion of privacy. Most notably, a protocol due to Le Gall (ToC 2012) with communication complexity $O(\sqrt{n})$, and a protocol by Kerenidis et al. (QIC 2016) with communication complexity $O(\log(n))$, and $O(n)$ shared entanglement. We show that, in a sense, input purification is the only potent adversarial strategy, and protocols such as the two protocols above are secure in a restricted variant of the quantum honest but curious (a.k.a specious) model. More explicitly, we propose a restricted privacy notion called \emph{anchored privacy}, where the adversary is forced to execute on a classical database (i.e. the execution is anchored to a classical database). We show that for measurement-free protocols, anchored security against honest adversarial servers implies anchored privacy even against specious adversaries. Finally, we prove that even with (unlimited) pre-shared entanglement it is impossible to achieve security in the standard specious model with sub-linear communication, thus further substantiating the necessity of our relaxation. This lower bound may be of independent interest (in particular recalling that PIR is a special case of Fully Homomorphic Encryption)

Dark Energy Survey year 1 results: cosmological constraints from cluster abundances and weak lensing

We perform a joint analysis of the counts and weak lensing signal of redMaPPer clusters selected from the Dark Energy Survey (DES) Year 1 dataset. Our analysis uses the same shear and source photometric redshifts estimates as were used in the DES combined probes analysis. Our analysis results in surprisingly low values for S8=σ8(Ωm/0.3)0.5=0.65±0.04, driven by a low matter density parameter, Ωm=0.179+0.031−0.038, with σ8−Ωm posteriors in 2.4σ tension with the DES Y1 3x2pt results, and in 5.6σ with the Planck CMB analysis. These results include the impact of post-unblinding changes to the analysis, which did not improve the level of consistency with other data sets compared to the results obtained at the unblinding. The fact that multiple cosmological probes (supernovae, baryon acoustic oscillations, cosmic shear, galaxy clustering and CMB anisotropies), and other galaxy cluster analyses all favor significantly higher matter densities suggests the presence of systematic errors in the data or an incomplete modeling of the relevant physics. Cross checks with x-ray and microwave data, as well as independent constraints on the observable-mass relation from Sunyaev-Zeldovich selected clusters, suggest that the discrepancy resides in our modeling of the weak lensing signal rather than the cluster abundance. Repeating our analysis using a higher richness threshold (λ≥30) significantly reduces the tension with other probes, and points to one or more richness-dependent effects not captured by our model

Bioreactor for microalgal cultivation systems: strategy and development

Microalgae are important natural resources that can provide food, medicine, energy and various bioproducts for nutraceutical, cosmeceutical and aquaculture industries. Their production rates are superior compared to those of terrestrial crops. However, microalgae biomass production on a large scale is still a challenging problem in terms of economic and ecological viability. Microalgal cultivation system should be designed to maximize production with the least cost. Energy efficient approaches of using light, dynamic mixing to maximize use of carbon dioxide (CO2) and nutrients and selection of highly productive species are the main considerations in designing an efficient photobioreactor. In general, optimized culture conditions and biological responses are the two overarching attributes to be considered for photobioreactor design strategies. Thus, fundamental aspects of microalgae growth, such as availability of suitable light, CO2 and nutrients to each growing cell, suitable environmental parameters (including temperature and pH) and efficient removal of oxygen which otherwise would negatively impact the algal growth, should be integrated into the photobioreactor design and function. Innovations should be strategized to fully exploit the wastewaters, flue-gas, waves or solar energy to drive large outdoor microalgae cultivation systems. Cultured species should be carefully selected to match the most suitable growth parameters in different reactor systems. Factors that would decrease production such as photoinhibition, self-shading and phosphate flocculation should be nullified using appropriate technical approaches such as flashing light innovation, selective light spectrum, light-CO2 synergy and mixing dynamics. Use of predictive mathematical modelling and adoption of new technologies in novel photobioreactor design will not only increase the photosynthetic and growth rates but will also enhance the quality of microalgae composition. Optimizing the use of natural resources and industrial wastes that would otherwise harm the environment should be given emphasis in strategizing the photobioreactor mass production. To date, more research and innovation are needed since scalability and economics of microalgae cultivation using photobioreactors remain the challenges to be overcome for large-scale microalgae production