Scientific Series

This is a talk in two parts. The first part is on evolution of a system under a Hamiltonian. First, a general method for implementing evolution under a Hamiltonian using entanglement and classical communication is presented. This method improves on previous methods by requiring less entanglement and communication, as well as allowing more general Hamiltonians to be implemented. Next, a method for simulating evolution under a sparse Hamiltonian using a quantum computer is presented. When H acts on n qubits, and has at most a constant number of nonzero entries in each row/column, we may select any positive integer k such that the simulation requires O((log*n)t^(1+1/2k)) accesses to matrix entries of H. The second part of the talk is on adaptive measurements of optical phase. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/sqrt(N). It has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N. I present a Heisenberg-limited phase estimation procedure which has been demonstrated experimentally. We use multiple applications of the phase shift on unentangled single-photon states, and generalize Kitaev\\\'s phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit.

We define a measure of the quantumness of correlations, based on the operative task of local broadcasting of a bipartite state. Such a task is feasible for a state if and only if it corresponds to a joint classical probability distribution, or, in other terms, it is strictly classically correlated. A gap, defined in terms of quantum mutual information, can quantify the degree of failure in fulfilling such a task, therefore providing a measure of how non-classical a given state is. We are led to consider the asymptotic average mutual information of a state, defined as the minimal per-copy mutual information between parties, when they share an infinite amount of broadcast copies of the state. We analyze the properties of such quantity, and find that it satifies many of the properties required for an entanglement measure. We show that it lies between the quantum- and the classical-conditioned versions of squashed entanglement. The non-vanishing of asymptotic average mutual information for entangled states may be interpreted as a signature of monogamy of entanglement.

We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability 1 - p. 2. At each stage k comparisons can be performed in parallel and a noisy answer is returned. We present a (classic) algorithm which optimally solves both variants together, up to an additive term of O(log log (n)), and prove matching information theoretic lower bounds. We use the algorithm with the results of Farhi et al. (FGGS99)presenting a quantum search algorithm in an ordered list of expected complexity less than log(n)/3, and some improved quantum lower bounds on noisy search, and search with an error probability. Joint work with Michael Ben-Or.

After almost a century of observations, the ultra-high energy sky has finally displayed an anisotropic distribution. A significant correlation between the arrival directions of ultra-high cosmic rays measured by the Pierre Auger Observatory and the distribution of nearby active galactic nuclei signals the dawn of particle astronomy. These historic results have important implications to both astrophysics and particle physics.

Roughly speaking, the more Alice is entangled with Bob, the harder it is for her to send her state to Charlie. In particular, it will be shown that the squashed entanglement, a well known entanglement measure, gives the fastest rate at which a quantum state can be sent between two parties who share arbitrary side information. Likewise, the entanglement of formation and entanglement cost is shown to be the fastest rate at which a quantum state can be sent when the parties have access to side-information which is maximally correlated. A further restriction on the type of side-information implies that the rate of state transmission is given by the quantum mutual information. This suggests a new paradigm for understanding entanglement and other correlations in terms of quantum Shannon theroy. Different types of side-information correspond to different types of correlations with the squashed entanglement and the mutual information being two extremes. Furthermore, there is a dual paradigm: if one distributes the side-information as aliciously as possible so as to make the sending of the state as difficult as possible, one finds maximum rates which give interpretations to known quantities as well as new ones.

In any attempt to construct a Quantum Theory of Gravity, one has to deal with the fact that Time in Quantum Mechanics appears to be very different from Time in General Relativity. This is the famous (or actually notorious!) \"Problem of Time\", and gives rise to both conceptual and technical problems. The decoherent histories approach to quantum theory, is an alternative formulation of quantum theory specially designed to deal with closed (no-external observer or environment) systems. This approach has been considered particularly promising, in dealing with the problem of time, since it puts space and time in equal footing (unlike standard QM) . This talk develops a particular implementation of the above expectations, i.e. we construct a general set of \"Class Operators\" corresponding to questions that appear to be \"Timeless\" (independent of the parameter time), but correspond to physically interesting questions. This is similar to finding a general enough set of timeless observables, in the evolving constants approach to the problem of time.

I will describe the emergence of geometric (Berry) phases in supersymmetric systems. In theories with degenerate states, non-Abelian geometric phases can arise. I show how supersymmetry helps to ensure the existence of this phenomenon by invoking the examples of systems with (2,2) and (4,4) supersymmetry. In the former, I show how instantons contribute crucially to the form of the non-Abelian phase. The latter system applies to D0-D4 brane dynamics in string theory, leading to a surprising re-interpretation of the Berry phase in terms of gravitational precession of a probe brane. Towards the end will comment on some work in progress on the geometric phase in (8,8) SUSY systems.

Some thirty years ago surface-enhanced Raman (SERS) was discovered. In a nutshell, molecules positioned near roughened silver and gold surfaces were found to produce Raman spectra some 6 orders more intense than what an equivalent number of solution-phase molecules did. A large number of mechanisms were proposed to account for this spectacular effect, among which the one that seems to account for most of the observations essentially ascribes SERS to the concentration of the optical field in appropriately structured, interacting nanoscale features which operate both on the incident and Raman-scattered light. This concentration is to be appreciable only for features in which strong and narrow localized surface plasmons were excited. This “plasmonic” model not only accounted for many of SERS seminal features but also gave birth to the research fields of plasmonics and so-called metamaterials most of which achieve the necessary conditions governing the electrical permittivity and magnetic susceptibility of metamaterials in wavelength regions where plasmons are excited. SERS was again in the news approximately 10 years ago when a number of groups pointed out that SERS from individual molecules could be observed leading some to speculate that this observation challenged the plasmonic origin of SERS. The discovery of single-molecule SERS, coincident with the intense interest of the research community in nanoscience and technology, produced a renaissance of interest in SERS that is still with us. The work of the past half dozen years reaffirmed SERS as ultimately a plasmonic effect wherein most SERS-active systems are actually rather heterogeneous with most of the enhancement originating from “hot spots” where the enhancement could top 10 orders of magnitude averaged over territory where the enhancement is rather low. The major current challenge in the field is to devise nanostructures where the hot spots dominate, leading to systems with an inordinate ability to focus electromagnetic fields so as to produce not only extraordinarily intense SERS (presumably as a super-sensitive chemical analysis tool) but also as loci where other unusual photo-induced physical and chemical processes occur when the system is illuminated with rather banal light sources. The talk will illustrate some of the most recent advances in this field.

We attempt at characterizing the correlations present in the quantum computational model DQC1, introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. Although there is little or no entanglement between two parts of this system, it provides an exponential speedup in certain problems. On the contrary, we find that the quantum discord across the most natural split is nonzero for typical instances of the DQC1 ciruit. Nonzero values of discord indicate the presence of nonclassical correlations. We propose quantum discord as figure of merit for characterizing the resources present in this computational model. This might be a complementary measure for counting resources in quantum information science.

The Cosmic Microwave Background (CMB) consists of a bath of photons emitted when the universe was 380,000 years old. Carrying the imprint of primordial fluctuations that seeded the formation of structure in the universe, the CMB is one of the most valuable known tools for studying the early universe. In our modern, post WMAP era, the utility of studying temperature anisotropies in the CMB is clear and much of the work has been done. I will describe two exciting new directions in which the field is currently heading: small-scale secondary CMB anisotropy and CMB polarization anisotropy. In this context, I will briefly discuss preliminary results from our small-scale secondary anisotropy experiment, the Sunyaev-Zel\'dovich Array (SZA), and will describe our two upcoming CMB polarization experiments, the Q U Imaging ExperimenT (QUIET) and the E B EXperiment (EBEX).