Approximate Randomization of Quantum States With Fewer Bits of Key

Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon of the completely mixed state. Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004). Then, we show that a random sequence of essentially the same number of unitary operators, chosen from an appropriate set, with high probability form an approximately randomizing map for d-dimensional states. Finally, we discuss the optimality of these schemes via connections to different notions of pseudorandomness, and give a new lower bound for small epsilon.Comment: 18 pages, Quantum Computing Back Action, IIT Kanpur, March 2006, volume 864 of AIP Conference Proceedings, pages 18--36. Springer, New Yor

Small Pseudo-Random Families of Matrices: Derandomizing Approximate Quantum Encryption

A quantum encryption scheme (also called private quantum channel, or state randomization protocol) is a one-time pad for quantum messages. If two parties share a classical random string, one of them can transmit a quantum state to the other so that an eavesdropper gets little or no information about the state being transmitted. Perfect encryption schemes leak no information at all about the message. Approximate encryption schemes leak a non-zero (though small) amount of information but require a shorter shared random key. Approximate schemes with short keys have been shown to have a number of applications in quantum cryptography and information theory. This paper provides the first deterministic, polynomial-time constructions of quantum approximate encryption schemes with short keys. Previous constructions (quant-ph/0307104) are probabilistic--that is, they show that if the operators used for encryption are chosen at random, then with high probability the resulting protocol will be a secure encryption scheme. Moreover, the resulting protocol descriptions are exponentially long. Our protocols use keys of the same length as (or better length than) the probabilistic constructions; to encrypt $n$ qubits approximately, one needs $n+o(n)$ bits of shared key. An additional contribution of this paper is a connection between classical combinatorial derandomization and constructions of pseudo-random matrix families in a continuous space.Comment: 11 pages, no figures. In Proceedings of RANDOM 2004, Cambridge, MA, August 200

On the Coherence of WMAP and Planck Temperature Maps

The recent data release of ESA's Planck mission together with earlier WMAP releases provide the first opportunity to compare high resolution full sky Cosmic Microwave Background temperature anisotropy maps. To quantify the coherence of these maps beyond the power spectrum we introduce Generalized Phases, unit vectors in the (2l+1) dimensional representation spaces. For a Gaussian distribution, Generalized Phases are random and if there is non-Gaussianity, they represent most of the non-Gaussian information. The alignment of these unit vectors from two maps can be characterized by their angle, 0 deg expected for full coherence, and 90 deg for random vectors. We analyze maps from both missions with the same mask and Nside=512 resolution, and compare both power spectra and Generalized Phases. We find excellent agreement of the Generalize Phases of Planck Smica map with that of the WMAP Q,V,W maps, rejecting the null hypothesis of no correlations at 5 sigma for l's l<700, l<900 and l<1100, respectively, except perhaps for l<10. Using foreground reduced maps for WMAP increases the phase coherence. The observed coherence angles can be explained with a simple assumption of Gaussianity and a WMAP noise model neglecting Planck noise, except for low-intermediate l's there is a slight, but significant off-set, depending on WMAP band. On the same scales WMAP power spectrum is about 2.6% higher at a very high significance, while at higher l's there appears to be no significant bias. Using our theoretical tools, we predict the phase alignment of Planck with a hypothetical perfect noiseless CMB experiment, finding decoherence at l > 2900; below this value Planck can be used most efficiently to constrain non-Gaussianity.Comment: 8 pages, 8 figures, accepted for publication in MNRAS; minor modifications and 2 new figures adde

A new method for constructing small-bias spaces from Hermitian codes

We propose a new method for constructing small-bias spaces through a combination of Hermitian codes. For a class of parameters our multisets are much faster to construct than what can be achieved by use of the traditional algebraic geometric code construction. So, if speed is important, our construction is competitive with all other known constructions in that region. And if speed is not a matter of interest the small-bias spaces of the present paper still perform better than the ones related to norm-trace codes reported in [12]

Quantifying biogenic bias in screening libraries.

In lead discovery, libraries of 10(6) molecules are screened for biological activity. Given the over 10(60) drug-like molecules thought possible, such screens might never succeed. The fact that they do, even occasionally, implies a biased selection of library molecules. We have developed a method to quantify the bias in screening libraries toward biogenic molecules. With this approach, we consider what is missing from screening libraries and how they can be optimized

Oppressive Things

In analyzing oppressive systems like racism, social theorists have articulated accounts of the dynamic interaction and mutual dependence between psychological components, such as individuals’ patterns of thought and action, and social components, such as formal institutions and informal interactions. We argue for the further inclusion of physical components, such as material artifacts and spatial environments. Drawing on socially situated and ecologically embedded approaches in the cognitive sciences, we argue that physical components of racism are not only shaped by, but also shape psychological and social components of racism. Indeed, while our initial focus is on racism and racist things, we contend that our framework is also applicable to other oppressive systems, including sexism, classism, and ableism. This is because racist things are part of a broader class of oppressive things, which are material artifacts and spatial environments that are in congruence with an oppressive system

Between food ethics, solidarity and the social construction of alternative markets. Exploring the dimensions of grassroots food movements in Spain

In recent years there has been growing attention for the emergence of alternative food networks, first as a possible strategy for farm households to counter deteriorating market conditions and respond to changing societal demands, and more recently as expression of a growing consumer involvement in the shaping of food systems. In debates on AFNs contributions from Spain have been relatively scarce, not because these tendencies do not occur but rather because applied analytical frameworks somehow did not seem to capture the specific nature of experiences in the peninsula. Against this background, this paper aims to analyze emerging grassroots food movements in Spain, explore to what extent different initiatives constitute a coherent alternative paradigm for sustainable local food systems, and identify relevant dimensions that shape their development and potential contribution to the sustainable development of rural areas and society at large. The paper is mainly based on case studies from Andalucia and the Basque country, and stresses that food initiatives have been largely driven by social movements, incl. peasant‐based farmers and consumer groups but also agroecology movements. As a result, Spanish food movements often have a wider focus and combine ethical values like fairness, solidarity and participative democracy with economic and environmental concerns

Quantum Hashing for Finite Abelian Groups

We propose a generalization of the quantum hashing technique based on the notion of the small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for succinct quantum presentation of elements of any finite abelian group, which can be used in various computational and cryptographic scenarios. The known quantum fingerprinting schemas turn out to be the special cases of the proposed quantum hashing for the corresponding abelian group