Quantum Foundations

417 talks

S002

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Displaying 241 - 252 of 417

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
Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.

Ravi Kunjwal Funds for Scientific Research - FNRS
January 14, 2014

PIRSA:14010102
Quantum Foundations
Rebuilding Mathematics on a Quantum Logical Foundation

Richard deJonghe University of Illinois at Chicago
December 10, 2013

PIRSA:13120060
Quantum Foundations
Quantum Mechanics as Classical Physics

Charles Sebens University of Michigan–Ann Arbor
December 03, 2013

PIRSA:13120006
Quantum Foundations

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.
Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.

Ravi Kunjwal Funds for Scientific Research - FNRS
January 14, 2014

PIRSA:14010102
Quantum Foundations
The purpose of this talk is twofold: First, following Spekkens, to motivate noncontextuality as a natural principle one might expect to hold in nature and introduce operational noncontextuality inequalities motivated by a contextuality scenario first considered by Ernst Specker. These inequalities do not rely on the assumption of outcome-determinism which is implicit in the usual Kochen-Specker (KS) inequalities. We argue that they are the appropriate generalization of KS inequalities, serving as a test for the possibility of noncontextual explanations of experimental data. This is very much in the spirit of Bell inequalities, which provide theory-independent tests for local hidden variable explanations of experimental data without relying on the assumption of outcome-determinism. The second purpose is to point out a curious feature of quantum theory, motivated by the connections between (in)compatibility and (non)contextuality: namely, that it admits all conceivable (in)compatibility relations between observables.
Rebuilding Mathematics on a Quantum Logical Foundation

Richard deJonghe University of Illinois at Chicago
December 10, 2013

PIRSA:13120060
Quantum Foundations
It is not unnatural to expect that difficulties lying at the foundations of quantum mechanics can only be resolved by literally going back and rethinking the quantum theory from first principles (namely, the principles of logic). In this talk, I will present a first-order quantum logic which generalizes the propositional quatum logic originated by Birkhoff and von Neumann as well as the standard classical predicate logic used in the development of virtually all of modern mathematics. I will then use this quantum logic to begin to build the foundations of a new ``quantum mathematics'' --- in particular a quantum set theory and a quantum arithmetic --- which has the potential to provide a completely new mathematical framework in which to develop the theory of quantum
mechanics.
Quantum Mechanics as Classical Physics

Charles Sebens University of Michigan–Ann Arbor
December 03, 2013

PIRSA:13120006
Quantum Foundations
On the face of it, quantum physics is nothing like classical physics. Despite its oddity, work in the foundations of quantum theory has provided some palatable ways of understanding this strange quantum realm. Most of our best theories take that story to include the existence of a very non-classical entity: the wave function. Here I offer an alternative which combines elements of Bohmian mechanics and the many-worlds interpretation to form a theory in which there is no wave function. According to this theory, all there is at the fundamental level are particles interacting via Newtonian forces. In this sense, the theory is classical. However, it is still undeniably strange as it posits the existence of many worlds. Unlike the many worlds of the many-worlds interpretation, these worlds are fundamental, not emergent, and are interacting, not causally isolated. The theory will be presented as a fusion of the many-worlds interpretation and Bohmian mechanics, but can also be seen as a foundationally clear version of quantum hydrodynamics. A key strength of this theory is that it provides a simple and compelling story about the connection between the amplitude-squared of the wave function and probability. The theory also gives a natural explanation of the way the wave function transforms under time reversal and Galilean boosts.

Title	Speaker(s)	Date	Talk Type	Info
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
Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.	Ravi Kunjwal	2014-01-14	Scientific Series	View details
Rebuilding Mathematics on a Quantum Logical Foundation	Richard deJonghe	2013-12-10	Scientific Series	View details
Quantum Mechanics as Classical Physics	Charles Sebens	2013-12-03	Scientific Series	View details

Quantum Foundations

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