**David Albert**, Columbia University

*The Quantum-Mechanical Measurement Problem and the Foundations of Statistical Mechanics*

**Markus Arndt**, University of Vienna

*Nanoparticle interferometry: experimental tests of the quantum superposition principle at high mass and complexity*

**Angelo Bassi**, University of Trieste

*Phenomenology of spontaneous wave-function collapse models*

Models of spontaneous wave function collapse make predictions, which are different from those of standard quantum mechanics. Indeed, these models can be considered as a rival theory, against which the standard theory can be tested, in pretty much the same way in which parametrized post-Newtonian gravitational theories are rival theories of general relativity. The predictions of collapse models almost coincide with those of standard quantum mechanics at the microscopic level, as these models have to account for the microscopic world, as we know it. Departures become significant when the size of the system increases. However, for larger systems environmental influences become more and more difficult to eliminate. This is the reason why it is tricky to test collapse models experimentally, and so far no decisive test has been performed. We will review the main phenomenological properties of collapse models, in particular the so-called amplification mechanics, as well as the main models, which are debated in the literature (GRW, CSL, QMUPL, DP). We will review the lower bounds on the collapse parameter, and more importantly the upper bounds set by available experimental data. This data come both from experimental tests on earth, and from cosmological observations.

**Daniel Bedingham**, Imperial College, London

*Energy diffusion from relativistic spontaneous localization*

We discuss energy diffusion due to spontaneous localization (SL) for a relativistically-fast moving particle. Based on evidence from relativistic extensions of SL we argue that non-relativistic SL should remain valid in the particle rest frame. This implies that calculations can be performed by transforming non relativistic results from the particle rest frame to the frame of the observer. We demonstrate this by considering a relativistic stream of non-interacting particles of cosmological origin and showing how their energy distribution evolves as they traverse the Universe. We present a solution and discuss the potential for astrophysical observations.

**Joseph Emerson**, Perimeter Institute & IQC

* Negative Quasi-Probability, Contextuality, Quantum Magic and the Power of Quantum Computation*

I will describe a several new results establishing a compelling set of connections between negative quasi-probability in the discrete Wigner function, state-dependent contextuality, and the set of magic quantum states that enable universal quantum computation (and exponential speed-up) in the presence of noise. These results hold for systems of odd-prime dimensional qudits, for which they establish strong connections between previously disparate notions of non-classicality.

**Richard Healey**, University of Arizona

*Why look beyond quantum theory?*

Quantum theory does not define its own landscape. We structure the landscape in response to some contemplated inadequacy of quantum theory. Much foundational work has been motivated by perceived conceptual inadequacies associated with non-locality and the measurement problem. By denying the descriptive function of the quantum state a pragmatist approach may free quantum theory of every conceptual flaw, only to highlight questions we can’t use the theory to address. We should seek to populate the quantum landscape with theories we could use to answer these questions.

**Joseph Henson**, Imperial College, London

*Characterizing quantum non-locality: a histories approach*

Characterising quantum non-locality using simple physical principles has become a hot topic in quantum foundations of late. In the simpler case of local hidden variable models, the space of allowed correlations can be characterised by requiring that there exists a joint probability distribution over all possible experimental outcomes, from which the experimental probabilities arise as marginals. This follows from Bell’s causality condition. But the existing characterisations of quantum correlations are far from being so straightforward. Motivated by a histories outlook, we propose the following condition: there exists a positive semi-definite matrix in which the indices run over all possible experimental outcomes, from which the experimental probabilities arise as “marginals” in a similar way. This is a much simpler condition than the usual statement of the existence of a quantum model for the probabilities, and suggests an underlying connection with Bell’s derivation of his bound on local correlations. I will outline existing proofs that this condition places strong bounds on correlations consistent with QM, and ask whether it could completely characterise quantum non-locality.

**Adrian Kent**, Perimeter Institute & University of Cambridge

*Path Integrals, Reality and Generalizations of Quantum Theory*

I describe some tentative new ideas on modified versions of quantum theory motivated by the path integral formalism, and on other generalizations, and comment on possible experimental implications.

**Wayne Myrvold**, Perimeter Institute & University of Western Ontario

*Ontology of collapse theories*

The textbook collapse postulate says that, after a measurement, the quantum state of the system on which the measurement was performed , and becomes an eigenstate of the observable measured. Naively, this is what one would expect of dynamical collapse theories. What one gets, instead, is an approximation to such eigenstates. This leaves us with the question of how to interpret such theories as representing a macroscopically definite world. In this talk, I will review some approaches to the ontology of collapse theories, and raise the question: do these yield rival accounts of the nature of the physical world, or are they mere choices of how to hang talk about ordinary objects onto a theory whose physical import is already clear?

**Philip Pearle**, Hamilton College

*Collapse and Consequences*

I shall give an introduction to conceptual ideas and equations of the CSL (Continuous Spontaneous Localization) theory of dynamical wave function collapse. Then, I shall discuss various applications of the theory.

**Renato Renner**, ETH Zurich

*On the non-extendibility of quantum theory*

I will present a recent theorem that asserts that there cannot exist an "extension of quantum theory" that allows us to make more informative predictions about future measurable events (e.g., whether a horizontally polarized photon passes a polarization filter with a given orientation) than standard quantum theory. The theorem is based on two assumptions about the extended theory: (i) the theory should be compatible with quantum theory (this means, in practice, that the theory is not falsified by current experimental data); (ii) the theory should not preclude experimenters from freely choosing the measurement settings. More precisely, the latter assumption corresponds to the requirement that measurement settings can be chosen at random such that they are independent of any other events, except of course those that lie in the causal future of the choice (i.e., in its future light cone). In addition, I will discuss a corollary of the non-extendibility theorem which leads to the same conclusions as a recent theorem by Pusey, Barrett, and Rudolph on the "reality of the quantum state", based only on the above assumptions.

**Lee Smolin**, Perimeter Institute

*Time, cosmology and quantum foundations*

I argue that quantum mechanics cannot usefully be extended to a theory of the whole universe, so the task of quantum foundations is to discover that cosmological theory which reduces to quantum mechanics when restricted to small subsystems of the universe. I argue that that cosmological theory will be based on a global notion of physical time which implies the distinction between past, present and future is real and objective. These motivate two examples of novel formulations of quantum theory: the real ensemble formulation and the principle of precedence. Each may imply departures from the expected quantum evolution for sufficiently large and complex quantum systems.

**Petros Wallden**, TEI Chalkida, Greece & National Kapodistrian University of Athens

*Towards a realist's interpretation of the path integral*

Having a fundamental spacetime view of physics, appears more justified in attempting to construct a quantum theory of gravity. In this talk, motivated by the latter, a path integral approach is adopted and an attempt to construct a self-consistent realistic histories formulation of quantum theory is presented. After revising the histories viewpoint of classical physics, the quantum case is considered. However, the nature of the probabilities arising from the path integral, leads us to alter the classical picture. The new ontology is that of a coevent (or a coarse grained history), and we analyse the consequences of this (relatively) novel proposal.

**Alex Wilce**, Susquehanna University

*Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory*

The last few years have seen a spate of operational or information-theoretic derivations (or \reconstructions") of nite-dimensional quantum mechanics [1]. These rest of some strong assumptions. In particular, most assume the state of a composite system is entirely determined by the joint probabilities it assigns to the outcomes of measurements on the component systems. This condition, often called local tomography, is satis ed by neither real nor quaternionic quantum theory. If we are interested in the possibilities for theories more general than orthodox quantum mechanics, we might wish to relax this constraint. In this talk I will discuss a weaker system of assumptions, involving correlations between a probabilistic system and an isomorphic conjugate system, that leads to a representation of such systems in terms of euclidean Jordan algebras [2]. These have a well-known classi cation as direct sums of real, complex or quaternionic quantum systems, possibly the exceptional Jordan algebra, and spin factors. The last are a form of \bit", characterized by a family of two-valued observables, parametrized by antipodal vectors in a sphere of arbitrary dimension. Orthodox quantum mechanics can be singled out by imposing local tomography, plus the existence of a qubit as additional axioms [3]. However, there is a natural way to form non-signaling, but generally non-locally tomo-graphic, composites of systems based on special euclidean Jordan algebras (that is, excluding the exceptional one). This yields a probabilistic theory strictly, but not wildly, more general than orthodox nite-dimensional QM; one that elegantly uni es real, complex and quaternionic quantum theory, has a simple operational basis, and allows for a spectrum of bits more general than permitted in orthodox quantum theory. Parts of this talk reflect ongoing joint work with Howard Barnum, Matthew Graydon and Cozmin Ududec.

References:

[1] G. Chiribella, M. D'Ariano and P. Perinotti, Phys. Rev. A 84, (2011), 012311-012350; B. Dakic and C. Brukner, in H. Halvorson (ed.), Deep Beauty, Cambridge, 2011; P. Goyal, Phys. Rev. A 78 (2008), 052120-052146; L. Hardy, arXiv:quant- ph/0101012 (2001); L. Masanes and M. Mueller, New J. Phys. 13 (2011) ; J. Rau, Annals of Physics 324 (2009) 2622{2637;

[2] A. Wilce, Conjugates, correlation and quantum mechanics, arXiv:1206.2897 (2012)

[3] H. Barnum and A. Wilce, Local tomography and the Jordan structure of quantum theory, arXiv:1202.4513, (2012)