Estimating operator norms using covering nets

We present several polynomial- and quasipolynomial-time approximation schemes for a large class of generalized operator norms. Special cases include the $2\rightarrow q$ norm of matrices for $q>2$, the support function of the set of separable quantum states, finding the least noisy output of entanglement-breaking quantum channels, and approximating the injective tensor norm for a map between two Banach spaces whose factorization norm through $\ell_1^n$ is bounded. These reproduce and in some cases improve upon the performance of previous algorithms by Brand\~ao-Christandl-Yard and followup work, which were based on the Sum-of-Squares hierarchy and whose analysis used techniques from quantum information such as the monogamy principle of entanglement. Our algorithms, by contrast, are based on brute force enumeration over carefully chosen covering nets. These have the advantage of using less memory, having much simpler proofs and giving new geometric insights into the problem. Net-based algorithms for similar problems were also presented by Shi-Wu and Barak-Kelner-Steurer, but in each case with a run-time that is exponential in the rank of some matrix. We achieve polynomial or quasipolynomial runtimes by using the much smaller nets that exist in $\ell_1$ spaces. This principle has been used in learning theory, where it is known as Maurey's empirical method.Comment: 24 page

Quantum de Finetti Theorems under Local Measurements with Applications

Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements one can get a much improved error dependence on the dimension of the subsystems. We also obtain similar results for non-signaling probability distributions. We give the following applications of the results: We prove the optimality of the Chen-Drucker protocol for 3-SAT, under the exponential time hypothesis. We show that the maximum winning probability of free games can be estimated in polynomial time by linear programming. We also show that 3-SAT with m variables can be reduced to obtaining a constant error approximation of the maximum winning probability under entangled strategies of O(m^{1/2})-player one-round non-local games, in which the players communicate O(m^{1/2}) bits all together. We show that the optimization of certain polynomials over the hypersphere can be performed in quasipolynomial time in the number of variables n by considering O(log(n)) rounds of the Sum-of-Squares (Parrilo/Lasserre) hierarchy of semidefinite programs. As an application to entanglement theory, we find a quasipolynomial-time algorithm for deciding multipartite separability. We consider a result due to Aaronson -- showing that given an unknown n qubit state one can perform tomography that works well for most observables by measuring only O(n) independent and identically distributed (i.i.d.) copies of the state -- and relax the assumption of having i.i.d copies of the state to merely the ability to select subsystems at random from a quantum multipartite state. The proofs of the new quantum de Finetti theorems are based on information theory, in particular on the chain rule of mutual information.Comment: 39 pages, no figure. v2: changes to references and other minor improvements. v3: added some explanations, mostly about Theorem 1 and Conjecture 5. STOC version. v4, v5. small improvements and fixe

Optofluidic fabrication for 3D-shaped particles.

Complex three-dimensional (3D)-shaped particles could play unique roles in biotechnology, structural mechanics and self-assembly. Current methods of fabricating 3D-shaped particles such as 3D printing, injection moulding or photolithography are limited because of low-resolution, low-throughput or complicated/expensive procedures. Here, we present a novel method called optofluidic fabrication for the generation of complex 3D-shaped polymer particles based on two coupled processes: inertial flow shaping and ultraviolet (UV) light polymerization. Pillars within fluidic platforms are used to deterministically deform photosensitive precursor fluid streams. The channels are then illuminated with patterned UV light to polymerize the photosensitive fluid, creating particles with multi-scale 3D geometries. The fundamental advantages of optofluidic fabrication include high-resolution, multi-scalability, dynamic tunability, simple operation and great potential for bulk fabrication with full automation. Through different combinations of pillar configurations, flow rates and UV light patterns, an infinite set of 3D-shaped particles is available, and a variety are demonstrated

Citizen science and natural resource governance: program design for vernal pool policy innovation

Effective natural resource policy depends on knowing what is needed to sustain a resource and building the capacity to identify, develop, and implement flexible policies. This retrospective case study applies resilience concepts to a 16-year citizen science program and vernal pool regulatory development process in Maine, USA. We describe how citizen science improved adaptive capacities for innovative and effective policies to regulate vernal pools. We identified two core program elements that allowed people to act within narrow windows of opportunity for policy transformation, including (1) the simultaneous generation of useful, credible scientific knowledge and construction of networks among diverse institutions, and (2) the formation of diverse leadership that promoted individual and collective abilities to identify problems and propose policy solutions. If citizen science program leaders want to promote social-ecological systems resilience and natural resource policies as outcomes, we recommend they create a system for internal project evaluation, publish scientific studies using citizen science data, pursue resources for program sustainability, and plan for leadership diversity and informal networks to foster adaptive governance. Effective natural resource policy depends on knowing what is needed to sustain a resource and building the capacity to identify, develop, and implement flexible policies. This retrospective case study applies resilience concepts to a 16-year citizen science program and vernal pool regulatory development process in Maine, USA. We describe how citizen science improved adaptive capacities for innovative and effective policies to regulate vernal pools. We identified two core program elements that allowed people to act within narrow windows of opportunity for policy transformation, including (1) the simultaneous generation of useful, credible scientific knowledge and construction of networks among diverse institutions, and (2) the formation of diverse leadership that promoted individual and collective abilities to identify problems and propose policy solutions. If citizen science program leaders want to promote social-ecological systems resilience and natural resource policies as outcomes, we recommend they create a system for internal project evaluation, publish scientific studies using citizen science data, pursue resources for program sustainability, and plan for leadership diversity and informal networks to foster adaptive governance

Efficient Quantum Pseudorandomness

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum systems, but in many case pseudorandom operations can emulate certain properties of truly random ones. Indeed in the classical realm there is by now a well-developed theory of such pseudorandom operations. However the construction of such objects turns out to be much harder in the quantum case. Here we show that random quantum circuits are a powerful source of quantum pseudorandomness. This gives the for the first time a polynomialtime construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography and to understanding self-equilibration of closed quantum dynamics.Comment: 6 pages, 1 figure. Short version of http://arxiv.org/abs/1208.069

Entanglement can completely defeat quantum noise

We describe two quantum channels that individually cannot send any information, even classical, without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver.Comment: 4 pages, 1 figur

The cryptographic power of misaligned reference frames

Suppose that Alice and Bob define their coordinate axes differently, and the change of reference frame between them is given by a probability distribution mu over SO(3). We show that this uncertainty of reference frame is of no use for bit commitment when mu is uniformly distributed over a (sub)group of SO(3), but other choices of mu can give rise to a partially or even asymptotically secure bit commitment.Comment: 4 pages Latex; v2 has a new referenc

Radiation from a charge circulating inside a waveguide with dielectric filling

The emitted power of the radiation from a charged particle moving uniformly on a circle inside a cylindrical waveguide is considered. The expressions for the energy flux of the radiation passing through the waveguide cross-section are derived for both TE and TM waves. The results of the numerical evaluation are presented for the number of emitted quanta depending on the waveguide radius, the radius of the charge rotation orbit and dielectric permittivity of the filling medium. These results are compared with the corresponding quantities for the synchrotron radiation in a homogeneous medium.Comment: 10 pages, Latex, four EPS figure