Quantum Physics

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.

Ken Wharton An analysis of the path-integral approach to quantum theory motivates the hypothesis that two experiments with the same classical action should have dual ontological descriptions. If correct, this hypothesis would not only constrain realistic interpretations of quantum theory, but would also act as a constructive principle, allowing any realistic model of one experiment to generate a corresponding model for its action-dual. Two pairs of action-dual experiments will be presented, including one experiment that violates the Bell inequality and yet is action-dual to a single particle. Demanding a consistent, realistic ontology leads to a highly restricted parameter space of possible interpretations.

Wheeler's delayed choice (WDC) is one of the "standard experiments in foundations". It aims at the puzzle of a photon simultaneously behaving as wave and particle. Bohr-Einstein debate on wave-particle duality prompted the introduction of Bohr's principle of complementarity, ---`.. the study of complementary phenomena demands mutually exclusive experimental arrangements" . In WDC experiment the mutually exclusive setups correspond to the presence or absence of a second beamsplitter in a Mach-Zehnder interferometer (MZI). A choice of the setup determines the observed behaviour. The delay ensures that the behaviour cannot be adapted before the photon enters MZI. Using WDC as an example, we show how replacement of classical selectors by quantum gates streamlines experiments and impacts on foundational questions. We demonstrate measurements of complementary phenomena with a single setup, where observed behaviour of the photon is chosen after it has been already detected. Spacelike separation of the setup components becomes redundant. The complementarity principle has to be reformulated --- instead of complementarity of experimental setups we now have complementarity of measurement results. Finally we present a quantum-controlled scheme of Bell-type experiments.

Quantum correlations cannot be given any classical explanation that would satisfy Bell's local causality assumption. This quite intriguing feature of quantum theory, known as quantum non-locality, has fascinated physicists for years, and has more recently been proven to have interesting applications in quantum information processing. To properly understand the power of quantum non-locality, it is important to be able to quantify it. One way for that is to compare it to other "non-local resources", such as classical communication or "non-local Popescu-Rohrlich (PR) boxes", and try to use these alternative resources to reproduce the quantum correlations. I will review known results on this subject, and present new simulations of multipartite non-local correlations.

To model statistical correlations that violate Bell inequalities (such as singlet state correlations), one must relax at least one of three physically plausible postulates: measurement independence (experimenters can freely choose measurement settings independently of any underlying variables describing the system); no-signalling (underlying marginal distributions for one observer cannot depend on the measurement setting of a distant observer), and determinism (all outcomes can be fully determined by the values of underlying variables). It will be shown that, for any given model, one may quantify the degrees of measurement dependence, signalling and indeterminism, by three numbers M, S and I. It will further be shown how the Bell-CHSH inequality may be generalised to a "relaxed" Bell inequality, of the form ++-<=B(I,S,M), where the upper bound is tight and ranges between 2 and 4. The usual Bell-CHSH inequality corresponds to I=S=M=0. More generally, the bound B(I,S,M) quantifies the necessary mutual tradeoff between I, S and M that is required to model a given violation of the Bell-CHSH inequality. Some information-theoretic implications will be briefly described, as well as a no-signalling deterministic model of the singlet state that allows up to 86% experimental free will.

Karim Thebault Canonical quantization techniques are generally considered to provide one of the most rigorous methodologies for passing from a classical to a quantum description of reality. For classical Hamiltonian systems with constraints a number of such techniques are available (i.e. gauge fixing, Dirac constraint quantization, BRST quantization and geometric quantization) but all are arguably equivalent to the quantization of an underlying reduced phase space that parameterizes the "true degrees of freedom" and displays a symplectic geometric structure. The philosophical coherence of making any ontological investment in such a space for the case of canonical general relativity will be questioned here. Further to this, the particular example of Dirac quantization will be critically examined. Under the Dirac scheme the classical constraint functions are interpreted as quantum constraint operators restricting the allowed state vectors. For canonical general relativity this leads to the Wheeler-de Witt equation and the infamous problem of time but, prima facie, seems to rely on our interpretation of the classical Poisson bracket algebra of constraints as the phase space realization of the theory's local symmetries (i.e. the group of space-time diffeomorphisms). As with the construction of an interpretively viable symplectic reduced phase space, this straight forward connection between constraints and local symmetry will be questioned for the case of GR. These issues cast doubt on the basis behind the derivation of the so-called wave function of the universe and give us some grounds for re-examining the entire canonical quantum gravity program as currently constituted.

Shan Gao We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributed in space, proportional to the square of the absolute value of its wave function. If the wave function is a description of a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wave function, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations.

Maki Takahashi We present a formalism describing the transport of the quantum spin state of massive fermions in curved space-time for the purpose of studying relativistic quantum information phenomena such as entanglement and teleportation. We are concerned with answering the elementary question of how the state of a qubit transforms as it moves through a curved space-time manifold. This transport equation takes the form of the Fermi-Walker transport of a two component spinor, which will be shown to be unitary in the spinor's rest frame. The talk will summarise key results and highlight foundational issues such as the absence of global parallelism and conceptual issues/difficulties regarding entanglement and teleportation.

Quantum error correcting codes and topological quantum order (TQO) are inter-connected fields that study non-local correlations in highly entangled many-body quantum states. In this talk I will argue that each of these fields offers valuable techniques for solving problems posed in the other one. First, we will discuss the zero-temperature stability of TQO and derive simple conditions that guarantee stability of the spectral gap and the ground state degeneracy under generic local perturbations. These conditions thus can be regarded as a rigorous definition of TQO. Our results apply to any quantum spin Hamiltonian that can be written as a sum of geometrically local commuting projectors on a D-dimensional lattice. This large class of Hamiltonians includes Levin-Wen string-net models and Kitaev's quantum double models. Secondly, we derive upper bounds on the parameters of quantum codes with local check operators and discuss the implications for feasibility of a quantum self-correcting memory.

Tony Downes The geometry of space-time can only be determined by making measurements on physical systems. The ultimate accuracy achievable is then determined by quantum mechanics which fundamentally governs these systems. In this talk I will describe uncertainty principles constraining how well we can estimate the components of a metric tensor describing a gravitational field. I shall outline a number of examples which can be easily constructed with a minimum of mathematical complexity. I will also attempt to derive a general bound on the uncertainty in any attempt to determine the metric tensor which is expected to hold in an arbitrary globally hyperbolic space-time. I shall use tools developed within the algebraic approach to quantum field theory on a classical space-time background. I shall not consider limits on estimating space-time metrics that might arise from a quantisation of gravity itself.