Talks

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.

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.