Jeremy Butterfield
Introduction to quantum foundations

An introduction to the quantum measurement problem, including mention of (a) the density matrix formalism, reduced states, proper and improper mixtures; (b) decoherence; (c) the main strategies for solving the problem. 2) An introduction to quantum non-locality, including the EPR argument for extra values beyond the eigenstate-eigenvalue link, and proof of a Bell inequality (probably the Bell-Wigner inequality, and for stochastic hidden variable theories, the CHSH ) 3) An introduction to the broader philosophical currents: the isms of philosophy.

Robert Spekkens
Operationalism, hidden variable models, and contextuality

Preconceptions about the nature of reality can be significant impediments in attempts to understand and move beyond quantum theory.  In order to avoid such pitfalls, it is useful to characterize the theory entirely in terms of the observable consequences of experimental procedures, that is to say, operationally.  The scientific realist, however, is not happy to rest with such an interpretation of the quantum formalism.  She seeks to explain why certain detectors clicked at the rates that they did.  A natural model to explore is that the outcomes of quantum measurements are simply determined by (or at least their probabilities are determined by) the properties of physical systems that are fed into those devices.  Such models are known as hidden variable models.  Despite offering elegant explanations of many quantum phenomena, the simplest versions of these models --noncontextual versions -- cannot reproduce all of the predictions of quantum theory.  This is the Bell-Kochen-Specker theorem, one of the most significant results in quantum foundations. In addition to providing an introduction to all of these topics, I hope to describe an open question concerning hidden variable models and to present an operational generalization of the notion of contextuality which encompasses many of our best notions of nonclassicality.

Christopher Fuchs
Quantum States as Uncertainty, pure and simple.  But, Uncertainty about What?
 
David Deutsch implores us to "take quantum mechanics seriously."  In these lectures we will take quantum mechanics deadly seriously, but not in a way that would please Prof. Deutsch.  Here we lay the groundwork for viewing quantum mechanics as a branch of decision theory, specialized to decision-making agents immersed in an objective world of some particular characteristic---for need of a name, the quantum world.  That is to say, the view presented here is that quantum mechanics is less a direct picture of the world, and more a method of survival in it.  Its statements about the world are therefore oblique, but nonetheless firm and, from some points of view, more exciting because of the creative ontology they seem to hint at.

Topics of the lecture will include:  Einstein's pre-EPR argument for the incompleteness of quantum states, contrast between frequency and Bayesian interpretations of probability, Dutch book arguments for the structure of probability theory, the no-cloning and no-broadcasting theorems of quantum mechanics, classical no-cloning and yes-broadcasting examples, the quantum de Finetti representation theorem, the Kochen-Specker theorem, words on a Wolfgang Pauli'an style ontology in the light of Kochen-Specker, fiducial measurements for defining quantum states (for instance, SICs and MUBs), and the shape of quantum state space.

Wojciech Zurek
Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation

Starting with basic axioms of quantum theory we revisit  ``Relative State Interpretation'' set out 50 years ago by Hugh Everett III (1957a,b). His approach explains ``collapse of the wavepacket'' by postulating that observer perceives the state of the ``rest of the Universe'' {\it relative} to his own state, or -- to be more precise -- relative to the state of his records. This allows quantum theory to be universally valid. However, while Everett explains perception of collapse, relative state approach raises three questions absent in Bohr's Copenhagen Interpretation which relied on independent existence of an ab intio classical domain. One is now forced one to seek sets of preferred, effectively classical but ultimately quantum states that can define branches of the universal state vector, and allow observers to keep reliable records. Without such (i) preferred basis relative states are ``too relative'', and the approach suffers from basis ambiguity. Moreover, universal validity of quantum theory raises the issue of the (ii) origin of probabilities, and of the Born's rule  p_k = |\psi_k|^2 which is simply postulated in textbook discussions. Last not least, even preferred quantum states (defined e.g. by the einselection -- environment - induced superselection) -- are still quantum. Therefore they cannot be found out by initially ignorant observers through direct measurement without getting disrupted. Yet, states of macroscopic object exist objectively and can be found out by anyone. So, we need to identify the (iii) quantum origin of objective existence. Here we show how mathematical structure of quantum theory supplemented by the only uncontroversial measurement axiom (that demands immediate repeatability -- and, hence, predictability -- of idealized measurements) leads to preferred sets of states: Line of reasoning reminiscent of the  ``no cloning theorem'' yields  (i) pointer states which correspond to potential outcomes. Their stability is needed to establish effectively classical domain within quantum Universe, and to define events such as measurement outcomes. This leads one to enquire about their probabilities or -- more specifically -- about the relation between probabilities of measurement outcomes and the underlying quantum state. We show that symmetry of entangled states -  (ii) entanglement - assisted invariance or  envariance - implies Born's rule. It also accounts for the loss of physical significance of local phases between Schmidt states. (in essence, for decoherence). Thus, loss of coherence between pointer states is a consequence of symmetries of entanglement (e.g., with the environment). It can be established without usual tools of decoherence (reduced density matrices and trace operation) that rely on Born's rule for physical motivation. Finally, we point out that monitoring of the system by the environment (process responsible for decoherence) will typically leave behind multiple copies of its pointer states. Only states that can survive decoherence can produce information theoretic progeny in this manner. This (iii) quantum Darwinism allows observers to use  environment as a witness -- to acquire information about pointer states indirectly, leaving system of interest untouched and its state unperturbed. In conjunction with Everett's relative state account of the apparent collapse these advances illuminate relation of quantum theory to the classical domain of our experience. They complete existential interpretation based on the operational definition of objective existence, and justify our confidence in quantum mechanics as ultimate theory that needs no modifications to account for the emergence of the classical. They also suggest a reassessment of the relation between state vectors, physical reality and information, leading one to question objective existence of the “universal state vector”, at least in the absolute sense of Everett.

Sandu Popescu
Time symmetric quantum theory, weak measurements, and modular variables

Adrian Kent
Many-Worlds and One-World Interpretations of Quantum Theory

Benjamin Schumacher
Interaction and information flow between quantum systems

The transfer of information is a fundamental issue for quantum mechanics. In the two-slit experiment, interference between probability amplitudes is only observed if the particle is isolated from its environment. But the term “isolated” here does not mean that the particle is mechanically uncoupled from its environment. What it means is precisely that certain information is not transferred from the particle to the surrounding systems.

Information is also crucial for understanding what “locality” means in quantum dynamics. In order to predict the future state of a system, we do not need to know the past state of the entire universe, but only a local neighborhood of the system. This general fact is most easily expressed as a restriction on how information "flows" between systems. The interaction of two classical systems can result in a one-way information transfer, but for quantum systems the transfer of information must always proceed in both directions.

In this lecture I will describe a mathematical framework for discussing information flow between quantum systems and prove some general results about local quantum dynamics. Topics to be covered include: one-way information transfer in tripartite systems (for both unitary and generalized dynamics), how classical and quantum locality are related, structure results for quantum cellular automata, and a closer look at the information flow in the CNOT gate and other simple interactions.

Anthony Leggett
The quantum realization paradox: theoretical considerations and experimental input

Quantum mechanics has been enormously successful in describing nature at the atomic level,and most physicists believe that it is in principle the "whole truth" about the world even at the everyday level. However, such a view prima facie leads to a severe problem: in certain circumstances, the most natural interpretation of the theory implies that no definite outcome of an experiment occurs until the act of "observation". For many decades this problem was regard- ed as "merely philosophical", in the sense that it was thought that it had no consequences which could be tested in experiment. However, in the last dozen or so years the situation has changed very dramatically in this respect. I will discuss the problem, some popular "resolutions" of it, the current experimental situation and prospects for the future.