Quantum Foundations

408 talks

S002

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Quantum Foundations

Displaying 229 - 240 of 408

Classical statistics: resolving paradoxes since 1749

August 19, 2014

PIRSA:14080005
Inferring causal structure: a quantum advantage

Katja Ried
Universität Innsbruck
July 17, 2014

PIRSA:14070021
Quantum Foundations
Local quanta, unitary inequivalence, and vacuum entanglement

Hans Westman
May 20, 2014

PIRSA:14050117
Quantum Foundations
Physics, Logic and Mathematics of Time

Louis Kauffman
University of Illinois at Chicago
May 02, 2014

PIRSA:14050032
Quantum Foundations
Categories of Convex Sets and C*-Algebras

Robert Furber
Radboud Universiteit Nijmegen
April 15, 2014

PIRSA:14040140
Quantum Foundations
Beyond local causality: causation and correlation after Bell

Matthew Pusey
University of York
April 08, 2014

PIRSA:14040130
Quantum Foundations
Incompatibility of observables in quantum theory and other probabilistic theories
April 01, 2014

PIRSA:14040075
Quantum Foundations
Ambiguities in order-theoretic formulations of thermodynamics

Harvey Brown
University of Oxford
March 21, 2014

PIRSA:14030093
Quantum Foundations
A histories perpective on bounding quantum correlations

Joe Henson
BNP Paribas Asset Management London
March 18, 2014

PIRSA:14030111
Quantum Foundations
Seeing is Believing: Direct Observation of a General Quantum State

Jeff Lundeen
University of Ottawa
March 17, 2014

PIRSA:14030110
Quantum Foundations
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states

Matthew Leifer
Chapman University
February 18, 2014

PIRSA:14020145
Quantum Foundations
Does the Quantum Particle know its own Energy?

Rafael Sorkin
Perimeter Institute for Theoretical Physics
January 21, 2014

PIRSA:14010106
Quantum Foundations

Classical statistics: resolving paradoxes since 1749

August 19, 2014

PIRSA:14080005

There has been renewed interest in the effect that pre and postselection has on the foundations of quantum theory. Often, but not solely, in conjunction with weak measurement, pre and postselection scenarios are said to simultaneous create and resolve paradoxes. These paradoxes are said to be profound quandaries which bring us closer to the resolving the mysteries of the quantum. Here I was show that the same effects are present in classical physics when postselection and disturbance are allowed. In particular, I will demonstrate that anomalous weak values and protective measurements are already present in classical theory, thereby showing that these effects do not represent something uniquely quantum nor something that ought to be thought of as paradoxical. This is joint work with Josh Combes and Matt Leifer.
Inferring causal structure: a quantum advantage

Katja Ried
Universität Innsbruck
July 17, 2014

PIRSA:14070021
Quantum Foundations
A fundamental question in trying to understand the world -- be it classical or quantum -- is why things happen. We seek a causal account of events, and merely noting correlations between them does not provide a satisfactory answer. Classical statistics provides a better alternative: the framework of causal models proved itself a powerful tool for studying causal relations in a range of disciplines. We aim to adapt this formalism to allow for quantum variables and in the process discover a new perspective on how causality is different in the quantum world. Causal inference is a central task in the context of causal models: given observed statistics over a set of variables, one aims to infer how they are causally related. Yet in the seemingly simple case of just two classical variables, this is impossible (unless one makes additional assumptions). I will show how the analogous task for quantum variables can be solved. This quantum advantage is reminiscent of the advantages that quantum mechanics offers in computing and communication, and may lead to similarly rich insights. Our scheme is corroborated by data obtained in collaboration with Kevin Resch's experimental group. Time permitting, I will also address other applications of the quantum causal models. arXiv:1406.5036
Local quanta, unitary inequivalence, and vacuum entanglement

Hans Westman
May 20, 2014

PIRSA:14050117
Quantum Foundations
In this work we develop a formalism for describing localised quanta for a real-valued Klein-Gordon field in a one-dimensional box [0, R]. We quantise the field using non-stationary local modes which, at some arbitrarily chosen initial time, are completely localised within the left or the right side of the box. In this concrete set-up we directly face the problems inherent to a notion of local field excitations, usually thought of as elementary particles. Specifically, by computing the Bogoliubov coefficients relating local and standard (global) quantizations, we show that the local quantisation yields a Fock space F^L which is unitarily inequivalent to the standard one F^G. In spite of this, we find that the local creators and annihilators remain well defined in the global Fock space F^G, and so do the local number operators associated to the left and right partitions of the box. We end up with a useful mathematical toolbox to analyse and characterise local features of quantum states in F^G . Specifically, an analysis of the global vacuum state |0_G> ∈ F^G in terms of local number operators shows, as expected, the existence of entanglement between the left and right regions of the box. The local vacuum |0_L> ∈ F^L , on the contrary, has a very different character. It is neither cyclic nor separating and displays no entanglement. Further analysis shows that the global vacuum also exhibits a distribution of local excitations reminiscent, in some respects, of a thermal bath. We discuss how the mathematical tools developed herein may open new ways for the analysis of fundamental problems in local quantum field theory.
Physics, Logic and Mathematics of Time

Louis Kauffman
University of Illinois at Chicago
May 02, 2014

PIRSA:14050032
Quantum Foundations
Consider discrete physics with a minimal time step taken to be
tau. A time series of positions q,q',q'', ... has two classical
observables: position (q) and velocity (q'-q)/tau. They do not commute,
for observing position does not force the clock to tick, but observing
velocity does force the clock to tick. Thus if VQ denotes first observe
position, then observe velocity and QV denotes first observe velocity,
then observe position, we have
VQ: (q'-q)q/tau
QV: q'(q'-q)/tau
(since after one tick the position has moved from q to q').
Thus [Q,V]= QV - VQ = (q'-q)^2/tau. If we consider the equation
[Q,V] = k (a constant), then k = (q'-q))^2/tau and this is recognizably
the diffusion constant that arises in a process of Brownian motion.
Thus, starting with the simplest assumptions for discrete physics, we are
lead to recognizable physics. We take this point of view and follow it
in both physical and mathematical directions. A first mathematical
direction is to see how i, the square root of negative unity, is related
to the simplest time series: ..., -1,+1,-1,+1,... and making the
above analysis of time series more algebraic leads to the following
interpetation for i. Let e=[-1,+1] and e'=[+1,-1] denote, as ordered
pairs, two phase-shifted versions of the alternating series above.
Define an operator b such that eb = be' and b^2 = 1. Regard b as a time
shifting operator. The operator b shifts the alternating series by one
half its period. Regard e' = -e and ee' = [-1.-1] = -1 (combining term by
term). Then let i = eb. We have ii = (eb)(eb) = ebeb = ee'bb = -1. Thus ii = -1
through the definition of i as eb, a temporally sensitive entity that
shifts it phase in the course of interacting with (a copy of) itself.
By going to i as a discrete dynamical system, we can come back to the
general features of discrete dynamical systems and look in a new way at
the role of i in quantum mechanics. Note that the i we have constructed is
already part of a simple Clifford algebra generated by e and b with
ee = bb = 1 and eb + be = 0. We will discuss other mathematical physical
structures such as the Schrodinger equation, the Dirac equation and the
relationship of a simple logical operator (generalizing negation) with
Majorana Fermions.
Categories of Convex Sets and C*-Algebras

Robert Furber
Radboud Universiteit Nijmegen
April 15, 2014

PIRSA:14040140
Quantum Foundations
The start of the talk will be an outline how the ordinary notions of quantum theory translate into the category of C*-algebras, where there are several possible choices of morphisms. The second half will relate this to a category of convex sets used as state spaces. Alfsen and Shultz have characterized the convex sets arising from state spaces C*-algebras and this result can be applied to get a categorical equivalence between C*-algebras and state spaces of C*-algebras which is a generalization of the equivalence between the Schroedinger and Heisenberg pictures.
Beyond local causality: causation and correlation after Bell

Matthew Pusey
University of York
April 08, 2014

PIRSA:14040130
Quantum Foundations
There is now a remarkable mathematical theory of causation. But applying this theory to a Bell scenario implies the Bell inequalities, which are violated in experiment. We alleviate this tension by translating the basic definitions of the theory into the framework of generalised probabilistic theories. We find that a surprising number of results carry over: the d-separation criterion for conditional independence (the no-signalling principle on steroids), and even certain quantitative limits on correlations. Finally, we begin a classification of the causal structures, such as the Bell scenarios, that are "interesting" from this perspective. Joint work with Joe Henson and Raymond Lal.
Incompatibility of observables in quantum theory and other probabilistic theories
April 01, 2014

PIRSA:14040075
Quantum Foundations
We introduce a new way of quantifying the degrees of incompatibility of two observables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories. This opens up a flexible way of comparing probabilistic theories with respect to the nonclassical feature of incompatibility. We show that quantum theory contains observables that are as incompatible as any probabilistic physical theory can have. In particular, we prove that two of the most common pairs of complementary observables (position and momentum; number and phase) are maximally incompatible. However, if one adopts a more refined measure of the degree of incompatibility, for instance, by restricting the comparison to binary observables, it turns out that there are probabilistic theories whose inherent degree of incompatibility is greater than that of quantum theory. Finally, we analyze the noise tolerance of the incompatibility of a pair of observables in a CHSH-Bell experiment.
Ambiguities in order-theoretic formulations of thermodynamics

Harvey Brown
University of Oxford
March 21, 2014

PIRSA:14030093
Quantum Foundations
Since the 1909 work of Carathéodory, an axiomatic approach to thermodynamics has gained ground which highlights the role of the the binary relation of adiabatic accessibility between equilibrium states. A feature of Carathédory's system is that the version therein of the second law contains an ambiguity about the nature of irreversible adiabatic processes, making it weaker than the traditional Kelvin-Planck statement of the law. This talk attempts first to clarify the nature of this ambiguity, by defining the arrow of time in thermodynamics by way of the Equilibrium Principle (``Minus First Law''). It then examines the extent to which the 1989 axiomatisation of Lieb and Yngvason shares the same ambiguity, despite proposing a very different approach to the second law.
A histories perpective on bounding quantum correlations

Joe Henson
BNP Paribas Asset Management London
March 18, 2014

PIRSA:14030111
Quantum Foundations
There has recently been much interest in finding simple principles that explain the particular sets of experimental probabilities that are possible with quantum mechanics in Bell-type experiments. In the quantum gravity community, similar questions had been raised, about whether a certain generalisation of quantum mechanics allowed more than quantum mechanics in this regard. We now bring these two strands of work together to see what can be learned on both sides.
Seeing is Believing: Direct Observation of a General Quantum State

Jeff Lundeen
University of Ottawa
March 17, 2014

PIRSA:14030110
Quantum Foundations
Central to quantum theory, the wavefunction is a complex distribution associated with a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of it through its use to calculate measurement outcome probabilities through the Born Rule. Tomographic methods can reconstruct the wavefunction from measured probabilities. In contrast, I present a method to directly measure the wavefunction so that its real and imaginary components appear straight on our measurement apparatus. I will also present new work extending this concept to mixed quantum states. This extension directly measures a little-known proposal by Dirac for a classical analog to a quantum operator. Furthermore, it reveals that our direct measurement is a rigorous example of a quasi-probability phase-space (i.e. x,p) distribution that is closely related to the Q, P, and Wigner functions. Our direct measurement method gives the quantum state a plain and general meaning in terms of a specific set of simple operations in the lab.
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states

Matthew Leifer
Chapman University
February 18, 2014

PIRSA:14020145
Quantum Foundations
The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (representing knowledge, information, or belief) or an ontic state (a direct reflection of reality)? In the ontological models framework, quantum states correspond to probability measures over more fundamental states of reality. The quantum state is then ontic if every pair of pure states corresponds to a pair of measures that do not overlap, and is otherwise epistemic. Recently, several authors have derived theorems that aim to show that the quantum state must be ontic in this framework. Each of these theorems involve auxiliary assumptions of varying degrees of plausibility. Without such assumptions, it has been shown that models exist in which the quantum state is epistemic. However, the definition of an epistemic quantum state used in these works is extremely permissive. Only two quantum states need correspond to overlapping measures and furthermore the amount of overlap may be arbitrarily small. In order to provide an explanation of quantum phenomena such as no-cloning and the indistinguishability of pure states, the amount of overlap should be comparable to the inner product of the quantum states. In this talk, I show, without making auxiliary assumptions, that the ratio of overlap to inner product must go to zero exponentially in Hilbert space dimension for some families of states. This is done by connecting the overlap to Kochen-Specker noncontextuality, from which we infer that any contextuality inequality gives a bound on the ratio of overlap to inner product.
Does the Quantum Particle know its own Energy?

Rafael Sorkin
Perimeter Institute for Theoretical Physics
January 21, 2014

PIRSA:14010106
Quantum Foundations
If a wave function does not describe microscopic reality then what does? Reformulating quantum mechanics in path-integral terms leads to a notion of ``precluded event" and thence to the proposal that quantal reality differs from classical reality in the same way as a set of worldlines differs from a single worldline. One can then ask, for example, which sets of electron trajectories correspond to a Hydrogen atom in its ground state and how they differ from those of an excited state. We address the analogous questions for simple model that replaces the electron by a particle hopping (in discrete time) on a circular lattice.

Title	Speaker(s)	Date	Talk Type	Info
Classical statistics: resolving paradoxes since 1749		2014-08-19	Scientific Series	View details
Inferring causal structure: a quantum advantage	Katja Ried	2014-07-17	Scientific Series	View details
Local quanta, unitary inequivalence, and vacuum entanglement	Hans Westman	2014-05-20	Scientific Series	View details
Physics, Logic and Mathematics of Time	Louis Kauffman	2014-05-02	Scientific Series	View details
Categories of Convex Sets and C*-Algebras	Robert Furber	2014-04-15	Scientific Series	View details
Beyond local causality: causation and correlation after Bell	Matthew Pusey	2014-04-08	Scientific Series	View details
Incompatibility of observables in quantum theory and other probabilistic theories		2014-04-01	Scientific Series	View details
Ambiguities in order-theoretic formulations of thermodynamics	Harvey Brown	2014-03-21	Scientific Series	View details
A histories perpective on bounding quantum correlations	Joe Henson	2014-03-18	Scientific Series	View details
Seeing is Believing: Direct Observation of a General Quantum State	Jeff Lundeen	2014-03-17	Scientific Series	View details
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states	Matthew Leifer	2014-02-18	Scientific Series	View details
Does the Quantum Particle know its own Energy?	Rafael Sorkin	2014-01-21	Scientific Series	View details

Quantum Foundations

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