The Euler current and relativistic parity odd transport

For a spacetime of odd dimensions endowed with a unit vector field, we introduce a new topological current that is identically conserved and whose charge is equal to the Euler character of the even dimensional spacelike foliations. The existence of this current allows us to introduce new Chern-Simons-type terms in the effective field theories describing relativistic quantum Hall states and (2+1) dimensional superfluids. Using effective field theory, we calculate various correlation functions and identify transport coefficients. In the quantum Hall case, this current provides the natural relativistic generalization of the Wen-Zee term, required to characterize the shift and Hall viscosity in quantum Hall systems. For the superfluid case this term is required to have nonzero Hall viscosity and to describe superfluids with non s-wave pairing.Comment: 24 pages. v2: added citations, corrected minor typos in appendi

Effective Field Theory of Relativistic Quantum Hall Systems

Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a term of topological nature, which couples the electromagnetic field with a topologically conserved current of $2+1$ dimensional relativistic fluid. In contrast to the Chern-Simons term, the new term involves the spacetime metric in a nontrivial way. We extract the predictions of the effective theory for linear electromagnetic and gravitational responses. For fractional quantum Hall states at the zeroth Landau level, additional holomorphic constraints allow one to express the results in terms of two dimensionless constants of topological nature.Comment: 4 page

From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups

We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem. By solving this problem, we find efficient quantum algorithms for a number of nonabelian hidden subgroup problems, including some for which no efficient algorithm was previously known: certain metacyclic groups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including the Heisenberg group, r=2). In particular, our results show that entangled measurements across multiple copies of hidden subgroup states can be useful for efficiently solving the nonabelian HSP.Comment: 18 pages; v2: updated references on optimal measuremen

Improving water productivity in agriculture in developing economies: in search of new avenues

Water ProductivityCrop productionWheatCottonEvapotranspirationEcnomic aspects

Generalized self-testing and the security of the 6-state protocol

Self-tested quantum information processing provides a means for doing useful information processing with untrusted quantum apparatus. Previous work was limited to performing computations and protocols in real Hilbert spaces, which is not a serious obstacle if one is only interested in final measurement statistics being correct (for example, getting the correct factors of a large number after running Shor's factoring algorithm). This limitation was shown by McKague et al. to be fundamental, since there is no way to experimentally distinguish any quantum experiment from a special simulation using states and operators with only real coefficients. In this paper, we show that one can still do a meaningful self-test of quantum apparatus with complex amplitudes. In particular, we define a family of simulations of quantum experiments, based on complex conjugation, with two interesting properties. First, we are able to define a self-test which may be passed only by states and operators that are equivalent to simulations within the family. This extends work of Mayers and Yao and Magniez et al. in self-testing of quantum apparatus, and includes a complex measurement. Second, any of the simulations in the family may be used to implement a secure 6-state QKD protocol, which was previously not known to be implementable in a self-tested framework.Comment: To appear in proceedings of TQC 201

Quantum algorithm for a generalized hidden shift problem

Consider the following generalized hidden shift problem: given a function f on {0,...,M − 1} × ZN promised to be injective for fixed b and satisfying f(b, x) = f(b + 1, x + s) for b = 0, 1,...,M − 2, find the unknown shift s ∈ ZN. For M = N, this problem is an instance of the abelian hidden subgroup problem, which can be solved efficiently on a quantum computer, whereas for M = 2, it is equivalent to the dihedral hidden subgroup problem, for which no efficient algorithm is known. For any fixed positive �, we give an efficient (i.e., poly(logN)) quantum algorithm for this problem provided M ≥ N^∈. The algorithm is based on the “pretty good measurement” and uses H. Lenstra’s (classical) algorithm for integer programming as a subroutine

Hamiltonian Oracles

Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.Comment: 16 pages, REVTeX 4 (minor corrections in v2

Some Implications on Amorphic Association Schemes

AMS classifications: 05E30, 05B20;amorphic association scheme;strongly regular graph;(negative) Latin square type;cyclotomic association scheme;strongly regular decomposition

Adiabatic Quantum Computing with Phase Modulated Laser Pulses

Implementation of quantum logical gates for multilevel system is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language.Comment: 19 pages, 6 figures, submitted to JOP