Talks

The de Broglie-Bohm pilot-wave program is an attempt to formulate quantum theory (including quantum field theory) as a theory without observers, by assuming that the wave-function is not the complete description of a system, but must be supplemented by additional variables (beables). Although many progress has been made in order to extend the pilot-wave theory to quantum field theory, a compelling ontology for quantum field theory is still lacking and the choice of beable is likely to be relevant for the study of quantum non-equilibrium systems and their relaxation properties (Valentini). The present work takes its root in the fact that in the standard model of particle physics, all fermions are fundamentally massless and acquire their bare mass when the Higgs field condenses. In our tentative to build a pilot-wave model for quantum field theory in which beables are attributed to massless fermions, we are naturally led to Weyl spinors and to Penrose's zig-zag picture of the electron. In my talk, I will sketch this tentative and insist on some of its remarkable properties: namely that a positive-energy massive Dirac electron can be thought of as a superposition of positive and negative energy Weyl spinors of the same helicity, and that the massive Dirac electron can in principle move luminally at all times. Based on a joint work with H. Wiseman.

The effects of closed timelike curves (CTCs) in quantum dynamics, and its consequences for information processing have recently become the subject of a heated debate. Deutsch introduced a formalism for treating CTCs in a quantum computational framework. He postulated a consistency condition on the chronology-violating systems which led to a nonlinear evolution on the systems that come to interact with the CTC. This has been shown to allow tasks which are impossible in ordinary linear quantum evolution, such as computational speed-ups over (linear) quantum computers, and perfectly distinguishing non-orthogonal quantum states. Bennett and co-authors have argued, on the other hand, that nonlinear evolution allows no such exotic effects. They argued that all proofs of exotic effects due to nonlinear evolutions suffer from a fallacy they called the " linearity trap". Here we review the argument of Bennett and co-authors and show that there is no inconsistency in assuming linearity at the level of a classical ensemble, even at the presence of nonlinear quantum evolution. In fact, this is required for the very existence of empirically verifiable nonlinear evolution. The arguments for exotic quantum effects are thus seen to be based on the necessity for a fundamental distinction between proper and improper mixtures in the presence of nonlinear evolutions. We show how this leads to an operationally well-defined version of the measurement problem that we call the "preparation problem".

Tim Ralph We consider quantum mechanical particles that traverse general relativistic wormholes in such a way that they can interact with their own past, thus forming closed timelike curves. Using a simple geometric argument we reproduce the solutions proposed by Deutsch for such systems. Deutsch's solutions have attracted considerable interest because they do not contain paradoxes, however, as originally posed, they do contain ambiguities. We show that these ambiguities are removed by following our geometric derivation.

Can a density matrix be regarded as a description of the physically real properties of an individual system? If so, it may be possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. Non-linear modifications to the evolution of a density matrix can be proposed, based upon this idea, to account for thermodynamic irreversibility. Traditional approaches to interpreting quantum phenomena assume that an individual system is described by a pure state, with density matrices arising only through a statistical mixture or through tracing out entangled degrees of freedom. Treating the density matrix as fundamental can affect the viability of some of these interpretations, and introducting thermodynamically motivated non-linearities will not, in themselves, help in solving the quantum measurement problem.

Feynman showed that the path of least action is determined by quantum interference. The interference may be viewed as part of a quantum algorithm for minimising the action. In fact, Lloyd describes the Universe as a giant quantum computer whose purpose is to calculate its own state. Could the direction of time that the universe is apparently following be determined by a quantum algorithm? The answer lies in the violation of time reversal (T) invariance that is being observed in an increasing number of particle accelerator experiments. The violation signifies a fundamental asymmetry between the past and future and calls for a major shift in the way we think about time. Here we show that processes which violate T invariance induce destructive interference between different paths that the universe can take through time. The interference eliminates all paths except for two that represent continuously forwards and continuously backwards time evolution. This suggests that quantum interference from T violation processes gives rise to the phenomenological unidirectional nature of time. A path consisting exclusively of forward steps gives the shortest path to a point which is in the forwards direction. The quantum interference, therefore, underlies a quantum algorithm that determines shortest path through time.

In an ontological model of quantum theory that is Bell-local, one can assume without loss of generality that the outcomes of measurements are determined deterministically by the ontic states (i.e. the values of the local hidden variables). The question I address in this talk is whether such determinism can always be assumed in a noncontextual ontological model of quantum theory, in particular whether it can be assumed for nonprojective measurements. While it is true that one can always represent a measurement by a deterministic response function by incorporating ancillary degrees of freedom into one's description (for instance those of the apparatus), I show that in moving to such a representation, one typically loses the warrant to apply the assumption of measurement noncontextuality. The implications for experimental tests of measurement noncontextuality will be discussed.

There has been a growing interest in electromagnetic counterparts to gravitational wave signals. Of particular interest here, are counterparts to gravitational wave signals from super-massive black hole mergers. We consider a circumbinary disk, hollowed out by torques from the binary, and provide an analytic solution to its response following merger. There are two changes to the potential which occur during the merger process: an axisymmetric mass-energy loss and asymmetric recoil kick given to the resulting super-massive black hole. With a brief literature search we argue that, for fiducial disk values and for black hole spins aligned and anti-aligned with the orbital angular momentum, throughout the majority of parameter space the mass loss well dominates the effects of the recoil kicks on the circumbinary disk. This, along with assuming vertical hydrodynamic equilibrium, reduces the problem to one dimension. Using a 1D hydrodynamical code we explore the majority of parameter space and describe the different possible flows. In the 1D case, we give analytic approximations for the locations of the first shocks, their strengths, and the final density after the disk has again reached a steady state. This allows one to determine the temperature jump across the shock front and determine the observability, modulo the yet unknown disk mass.

Traditionally, the focus on determining characteristic properties of quantum mechanics has been on properties such as entanglement. However, entanglement is a property of multiple systems. Another interesting question is to ask what properties are characteristic of single quantum systems. Two answers to this question are: 1.There is a continuous path of pure quantum states connecting any two quantum states [1], and, 2.Quantum mechanics is preparation noncontextual [2]. In this talk, I will discuss a link between these two answers to this question. In particular, I will establish some strict upper bounds on the maximum size of the set of quantum states that can be modelled in a preparation noncontextual, nonnegative theory and show that this set contains pure states that cannot be connected to any other pure state in the set. I will also discuss a common example of a preparation noncontextual model that allows negative values, namely, a discrete Wigner function, and establish necessary and sufficient conditions for bases of an arbitrary dimensional Hilbert space to have nonnegative Wigner functions, i.e., to admit a classical model. I will conclude with a discussion of some open problems. [1] L. Hardy, quant-ph/0101012v4 (2001). [2] R. W. Spekkens, Phys. Rev. A, 71, 052108 (2005)

Matt Palmer An explicit description of a physical system is necessarily written with respect to a particular reference frame. It is important to know how to adapt the description when a different, equally valid, reference frame is chosen. In the case of classical frames there is a well-defined covariance of the description. The question we want to address is: How can we extend this description of change of reference frame to the case where the frames are quantum objects? We study this problem within specific toy models, and approach it operationally. We define a procedure that will change the quantum reference frame with which a quantum system is described. We find this procedure induces decoherence in the system and is described by a non-unitary CP map, which is in interesting distinction to the reversible nature of the classical change of frame procedures.

Information theory provides a novel approach to study of the consequences of symmetry of dynamics which goes far beyond the traditional conservation laws and Noether's theorem. The conservation laws are not applicable to the dissipative and open systems. In fact, as we will show, even in the case of closed system dynamics if the state of system is not pure the conservation laws do not capture all the consequences of symmetry. Using information theoretic approach to this problem we introduce new quantities called asymmetry monotones, that if the system is closed they are constant of motion and otherwise, if the system is open, they are always non-increasing. We also explain how different results in quantum information theory can have non-trivial consequences about the symmetric dynamics of quantum systems.