Conference

Inferring a quantum system\'s state, from repeated measurements, is critical for verifying theories and designing quantum hardware. It\'s also surprisingly easy to do wrong, as illustrated by maximum likelihood estimation (MLE), the current state of the art. I\'ll explain why MLE yields unreliable and rank-deficient estimates, why you shouldn\'t be a quantum frequentist, and why we need a different approach. I\'ll show how operational divergences -- well-motivated metrics designed to evaluate estimates -- follow from quantum strictly proper scoring rules. This motivates Bayesian Mean Estimation (BME), and I\'ll show how it fixes most of the problems with MLE. I\'ll conclude with a couple of speculations about the future of quantum state and process estimatio

In stochastic treatments of the ERRB set-up, it is equivalent to impose Bell\'s inequalities, a local causality condition, or a certain \"non-contextual hidden variables\" condition. But these conditions are violated by quantum mechanics. On the other hand, it is possible to view quantum mechanics as part of \"quantum measure theory\", a generalization of probability measure theory that allows pair wise interferences between histories whilst banning higher order interference. In this setting, is may be possible find quantum analogues of the three stochastic conditions. Following this line of inquiry, we will see that quantum measure theory allows no stronger violations of Bell\'s inequalities than does standard quantum theory. We also gain some insights into how to define causality in quantum theory.

Quantum information theory has two equivalent mathematical conjectures concerning quantum channels, which are also equivalent to other important conjectures concerning the entanglement. In this talk I explain these conjectures and introduce recent results.

It is a fundamental property of quantum mechanics that non-orthogonal pure states cannot be distinguished with certainty, which leads to the following problem: Given a state picked at random from some ensemble, what is the maximum probability of success of determining which state we actually have? I will discuss two recently obtained analytic lower bounds on this optimal probability. An interesting case to which these bounds can be applied is that of ensembles consisting of states that are themselves picked at random. In this case, I will show that powerful results from random matrix theory may be used to give a strong lower bound on the probability of success, in the regime where the ratio of the number of states in the ensemble to the dimension of the states is constant. I will also briefly discuss applications to quantum computation (the oracle identification problem) and to the study of generic entanglement.

Ancillary state construction is a necessary component of quantum computing. Ancillae are required both for error correction and for performing universal computation in a fault-tolerant way. Computation to an arbitrary accuracy, however, is effectively achieved by increasing the number of qubits in order to suppress the variance in the expected number of errors. Thus, it is important to be able to construct very large ancillary states. Concatenated quantum coding provides a means of constructing ancillae of any size, but, this fact aside, concatenation is not a particularly efficient form of coding. More efficient codes exist, but these codes lack the substructure of concatenated codes that enables fault-tolerant preparation of large ancillae. In this talk I will discuss the advantages of coding in large blocks, both from the perspective of efficiency and analysis, and I will describe my progress in developing construction procedures for moderately large ancillae.

The Everett (many-worlds) interpretation has made great progress over the past 20-30 years, largely due to the role of decoherence in providing a solution to the preferred basis problem. This makes it a serious candidate for a realist solution to the measurement problem. A remaining objection to the Everett interpretation (and one that is often considered fatal) is that that interpretation cannot make adequate sense of quantum probabilities. Dvaid Deutsch and David Wallace have argued that, by applying decision theory to the case of a rational agent who believes in the many-worlds interpretation, we can prove that such agents _act as if_ the theory predicted objective probabilities in the sense of fundamental indeterminism, or ignorance of initial conditions. I raise the issue of whether or not this, if true, is all that the many-worlds theorist needs from \'probability\'. I first suggest a reason for thinking that the answer might be \'no\': the reason is that knowing how to act on the assumption that a given theory is true is prima facie irrelevant to the question of whether we have any reason to believe the theory in the first place. I then go on to offer a solution to this problem, drawing on resources from Bayesian confirmation theory. My conclusion is that the problem of probability in the Everett interpretation has been solved.

Hints from quantum gravity suggest that a preferred frame may actually exist. One way to accommodate such a frame in general relativity without sacrificing diffeomorphism invariance is to couple the metric to a dynamical, time like, unit-norm vector field--the "aether". I will discuss properties and observational tests of a class of such theories, including post-Newtonian effects and radiation from binary pulsar systems.