Scientific Series

The basic problem of much of condensed matter and high energy physics, as well as quantum chemistry, is to find the ground state properties of some Hamiltonian. Many algorithms have been invented to deal with this problem, each with different strengths and limitations. Ideas such as entanglement entropy from quantum information theory and quantum computing enable us to understand the difficulty of various problems. I will discuss recent results on area laws and use these to prove that we can use matrix product states to efficiently represent ground states for one-dimensional systems with a spectral gap, while certain other one-dimensional problems, without the gap assumption, almost certainly have no efficient way for us to even represent the ground state on a classical computer. I will also discuss recent results on higher-dimensional matrix product states, in an attempt to extend the remarkable success of matrix product algorithms beyond one dimension.

We consider a consistent construction of the supersymmetric action for a codimension-two brane in six-dimensional Salam-Sezgin supergravity. When the brane carries a tension, we supersymmetrize the brane tension action by introducing a localized Fayet-Iliopoulos term on the brane and modifying the bulk SUSY transformations. As a result, we find that among the axisymmetric vacua of the system, the unwarped background with football-shaped extra dimensions respects N=1 supersymmetry. We extend the analysis to include the brane multiplets with the couplings to the bulk fields.

In this talk, we will investigate the distinguishability of quantum operations from both discrete and continuous point of view. In the discrete case, the main topic is how we can identify quantum measurement apparatuses by considering the patterns of measurement outcomes. In the continuous case, we will focus on the efficiency of parameter estimation of quantum operations. We will discuss several methods that can achieve Heisenberg Limit and prove in some other cases the impossibility of breaking the Standard Quantum Limit. The general treatment of estimation of quantum operations also allows an investigation of the effect of noise on estimation efficiency.

As physicists, we have become accustomed to the idea that a theory\\\'s content is always most transparent when written in coordinate-free language. But sometimes the choice of a good coordinate system is very useful for settling deep conceptual issues. Think of how Eddington-Finkelstein coordinates settled the longstanding question of whether the event horizon of a Schwarzschild black hole corresponds to a real spacetime singularity or not. Similarly we believe for an information-oriented or Bayesian approach to quantum foundations: That one good coordinate system may (eventually!) be worth more than a hundred blue-in-the-face arguments. This talk will motivate and chronicle the search for one such candidate coordinate system---the so-called Symmetric Informationally Complete Measurement---which has caught the attention of a handful of us here at PI and a handful of our visitors.

Bell\\\'s theorem is commonly understood to show that EPR correlations are not explainable via a local hidden variable theory. But Bell\\\'s theorem assumes that the initial state of the particles is independent of the final detector settings. It has been proposed that this independence assumption might be undermined by a relativistically-allowed form of \\\"backward causation\\\", thereby allowing construction of a local hidden-variable model after all. In this talk, I will show that there is no backward causation model which yields the desired correlations. However, there are other physical scenarios yielding nontrivial nonlocal correlations which violated Bell\\\'s independence assumption. I will present two.

I shall review the potential relevance of antisymmetric tensor fields in physics, perhaps the most intriguing being a massive antisymmetric tensor as dark matter. Next, based on the most general quadratic action for the antisymmetric tensor field, I shall discuss what are possible extensions of Einstein\\\'s theory which include antisymmetric tensor field and thus torsion in a dynamical fashion.

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.