Quantum Foundations

401 talks

S002

Collection Type Series

Description This series consists of talks in the areas of Quantum Foundations.

Displaying 253 - 264 of 401

Neorealism and the Internal Language of Topoi

Sander Wolters Radboud Universiteit Nijmegen
March 12, 2013
PIRSA:13030107
Quantum Foundations
The universe as a process of unique events

Lee Smolin Perimeter Institute for Theoretical Physics
February 26, 2013
PIRSA:13020146
Quantum Foundations
The structure of meaning in natural language: a big money quantum foundations spin-off.

Bob Coecke Quantinuum
February 12, 2013
PIRSA:13020131
Quantum Foundations
A positive and local formalism for quantum theory

Robert Oeckl Universidad Nacional Autónoma De Mexico (UNAM)
February 05, 2013
PIRSA:13020125
Quantum Foundations
Quantum Chaos, Information Gain and Quantum Tomography.

Vaibhav Madhok Wilfrid Laurier University
December 11, 2012
PIRSA:12120036
Quantum Foundations
If no information gain implies no disturbance, then any discrete physical theory is classical

Corsin Pfister
December 04, 2012
PIRSA:12120016
Quantum Foundations
Principle of relativity for quantum theory

Marco Zaopo University of Pavia
November 20, 2012
PIRSA:12110073
Quantum Foundations
Quasiprobability representations of qubits

November 13, 2012
PIRSA:12110070
What's an unknown POVM, and what does a two qubit state look like?

Matthew Pusey University of York

November 06, 2012
PIRSA:12110068
What is a Wavefunction?

Wayne Myrvold Western University

November 01, 2012
PIRSA:12110060
Thermodynamics of correlated quantum systems and a generalized exchange fluctuation theorem.

David Jennings Imperial College London
October 23, 2012
PIRSA:12100105
Quantum Foundations
New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics

Tobias Fritz Universität Innsbruck
October 09, 2012
PIRSA:12100055
Mathematical physics

Neorealism and the Internal Language of Topoi

Sander Wolters Radboud Universiteit Nijmegen
March 12, 2013
PIRSA:13030107
Quantum Foundations
Crudely formulated, the idea of neorealism, in the way that Chris Isham and Andreas Doering use it, means that each theory of physics, in its mathematical formulation should share certain structural properties of classical physics. These properties are chosen to allow some degree of realism in the interpretation (for example, physical variables always have values). Apart from restricting the form of physical theories, neorealism does increase freedom in the shape of physical theories in another way. Theories of physics may be interpreted in other topoi than the category of sets and functions. In my talk I will concentrate on two topos models for quantum theory. The contravariant model of Butterfield, Isham and Doering on the one hand, and the covariant model of Heunen, Landsman and Spitters on the other. I will argue that when we think of the topoi as generalized categories of sets (i.e. when we use the internal perspective of the topoi at hand), these two models are closely related, and both resemble classical physics. I will assume no background knowledge in topos theory.
The universe as a process of unique events

Lee Smolin Perimeter Institute for Theoretical Physics
February 26, 2013
PIRSA:13020146
Quantum Foundations
The structure of meaning in natural language: a big money quantum foundations spin-off.

Bob Coecke Quantinuum
February 12, 2013
PIRSA:13020131
Quantum Foundations
A positive and local formalism for quantum theory

Robert Oeckl Universidad Nacional Autónoma De Mexico (UNAM)
February 05, 2013
PIRSA:13020125
Quantum Foundations
The general boundary formulation (GBF) is an atemporal, but spacetime local formulation of quantum theory. Usually it is presented in terms of the amplitude formalism, which, in the presence of a background time, recovers the pure state formalism of the standard formulation of quantum theory. After reviewing the essentials of the amplitude formalism I will introduce a new "positive formalism", which recovers instead a mixed state formalism. This allows to define general quantum operations within the GBF and opens it to quantum information theory. Moreover, the transition to the positive formalism eliminates operationally irrelevant structure, making the extraction of measurement probabilities more direct. As a consequence, the probability interpretation takes on a remarkably simple and compelling form. I shall describe implications of the positive formalism, both for our understanding of quantum theory and for the practical formulation of quantum theories. I also observe a certain convergence with Lucien Hardy's operator tensor formulation of quantum theory, on which I hope to comment
Quantum Chaos, Information Gain and Quantum Tomography.

Vaibhav Madhok Wilfrid Laurier University
December 11, 2012
PIRSA:12120036
Quantum Foundations
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In recent years, attempts have been made to address this question from the perspective of quantum information theory. It is in this spirit that we study the connection between quantum chaos and information gain in the time series of a measurement record used for quantum tomography. The record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on a large ensemble of identical systems. We find an increase in information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two.
If no information gain implies no disturbance, then any discrete physical theory is classical

Corsin Pfister
December 04, 2012
PIRSA:12120016
Quantum Foundations
(based on http://arxiv.org/abs/1210.0194) It has been suggested that nature could be discrete in the sense that the underlying state space of a physical system has only a finite number of pure states. For example, the Bloch ball of a single qubit could be discretized into small patches and only appear round to us due to experimental limitations. Here, we present a strong physical argument for the quantum theoretical property that every state space (even the smallest possible one, the qubit) has infinitely many pure states. We propose a simple physical postulate which dictates that in fact the only possible discrete theory is classical mechanics. More specifically, we postulate that no information gain implies no disturbance, or read in the contrapositive, that disturbance leads to some form of information gain. In a theory like quantum mechanics where we already know that the converse holds, i.e. information gain does imply disturbance, this can be understood as postulating an equivalence between disturbance and information gain. What is more, we show that non-classical discrete theories are still ruled out even if we relax the postulate to hold only approximately in the sense that no information gain only causes a small amount of disturbance. Finally, our postulate also rules out popular generalizations such as the PR-box that allows non-local correlations beyond the limits of quantum theory.
Principle of relativity for quantum theory

Marco Zaopo University of Pavia
November 20, 2012
PIRSA:12110073
Quantum Foundations
In a generic quantum experiment we have a given set of devices analyzing some physical property of a system. To each device involved in the experiment we associate a set of random outcomes corresponding to the possible values of the variable analyzed by the device. Devices have apertures that permit physical systems to pass through them. Each aperture is labelled as "input" or "output" depending on whether it is assumed that the aperture lets the system go inside or outside the device. Assuming a particular input/output structure for the devices involved in a generic experiment is equivalent to assume a particular causal structure for the space-time events constituted by the outcomes happening on devices. The joint probability distribution of these outcomes is usually predicted assuming an absolutely defined input/output structure of devices. This means that all observers of the experiment agree on whether an aperture is labelled as "input" or "output". In this talk we show that the mathematical formalism of quantum theory permits to predict the joint probability distribution of outcomes in a generic experiment in such a way that the input/output structure is indeed relative to an observer. This means that two observers of the same experiment can predict the joint probability distribution of outcomes assuming different input/output labels for the apertures. Since input/output structure is the causal structure of the space-time events constituting the outcomes involved in the experiment we conclude that in quantum theory, the causal structure of events may not be regarded as absolute but rather as relative to the observer. We finally point out that properly extending this concept to the cosmological domain could shed light on the problem of dark energy.
Quasiprobability representations of qubits

November 13, 2012
PIRSA:12110070

Negativity in a quasi-probability representation is typically interpreted as an indication of nonclassical behavior. However, this does not preclude bases that are non-negative from having interesting applications---the single-qubit stabilizer states have non-negative Wigner functions and yet play a fundamental role in many quantum information tasks. We determine what other sets of quantum states and measurements of a qubit can be non-negative in a quasiprobability representation, and identify nontrivial groups of unitary transformations that permute such states. These sets of states and measurements are analogous to the single-qubit stabilizer states. We show that no quasiprobability representation of a qubit can be non-negative for more than two bases in any plane of the Bloch sphere. Furthermore, there is a single family of sets of four bases that can be non-negative in an arbitrary quasiprobability representation of a qubit. We provide an exhaustive list of the sets of single-qubit bases that are nonnegative in some quasiprobability representation and are also closed under a group of unitary transformations, revealing two families of such sets of three bases. We also show that not all two-qubit Clifford transformations can preserve non-negativity in any quasiprobability representation that is non-negative for the computational basis. This is in stark contrast to the qutrit case, in which the discrete Wigner function is non-negative for all n-qutrit stabilizer states and Clifford transformations. We also provide some evidence that extending the other sets of non-negative single-qubit states to multiple qubits does not give entangled states.
What's an unknown POVM, and what does a two qubit state look like?

Matthew Pusey University of York

November 06, 2012
PIRSA:12110068

If probabilities represent knowledge, what is an "unknown
probability"? De Finetti's theorem licenses the view that it is simply a
convenient metaphor for a certain class of knowledge about a series of
events. There are quantum versions for "unknown states" and "unknown
channels". I will explain how "unknown measurements" can be rehabilitated
too.

I will then move to a totally different topic. The Bloch sphere is handy
for representing qubit states, but the equivalent for two qubits is
15-dimensional! I will advocate instead drawing the set of states that Bob
can steer Alice to, the "steering ellipsoid". I will show how entanglement
and discord look from this perspective, and outline a geometric
classification of separable two qubit states.
What is a Wavefunction?

Wayne Myrvold Western University

November 01, 2012
PIRSA:12110060

The fact that the quantum wavefunction of a many-particle system is a function on a high-dimensional configuration space, rather than on spacetime, has led some to suggest that any realist understanding of quantum mechanics must regard configuration space as more fundamental than spacetime. Worse, it seems that a wavefunction monist ontology cannot help itself to talk of "configuration space" at all, without particles for the configurations to be configurations of. The wavefunction, it might seem, threatens to become a function defined on a high-dimensional space whose relation to spacetime is obscure. I will argue that such worries are misplaced.
Thermodynamics of correlated quantum systems and a generalized exchange fluctuation theorem.

David Jennings Imperial College London
October 23, 2012
PIRSA:12100105
Quantum Foundations
I will discuss the central role of correlations in thermodynamic directionality, how strong correlations can distort the thermodynamic arrow and contrast these distortions in both the classical and quantum regimes. These distortions constitute non-linear entanglement witnesses, and give rise to a rich information-theoretic structure. I shall explain how these results are then cast into the language of fluctuation theorems to derive a generalized exchange fluctuation theorem, and discuss the limitations of such a framework.
New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics

Tobias Fritz Universität Innsbruck
October 09, 2012
PIRSA:12100055
Mathematical physics
I will give an idea of what category theory is and how it can be successfully applied in mathematics and the mathematical sciences by means of example. The example is a notion from mathematical logic formalizing the intuitive concept of "property". The new category-theoretical definition of this notion can physically be interpreted as a measurement. Unraveling this definition in particular categories can be regarded as defining the concept of "property" in different context, e.g. in classical, probabilistic and quantum physics, and in each case this recovers familiar things.
Disclaimer: Up to some differences in the technical details, all of this is work of Bart Jacobs. (See arXiv:1205.3940)

Title	Speaker(s)	Date	Talk Type	Info
Neorealism and the Internal Language of Topoi	Sander Wolters	2013-03-12	Scientific Series	View details
The universe as a process of unique events	Lee Smolin	2013-02-26	Scientific Series	View details
The structure of meaning in natural language: a big money quantum foundations spin-off.	Bob Coecke	2013-02-12	Scientific Series	View details
A positive and local formalism for quantum theory	Robert Oeckl	2013-02-05	Scientific Series	View details
Quantum Chaos, Information Gain and Quantum Tomography.	Vaibhav Madhok	2012-12-11	Scientific Series	View details
If no information gain implies no disturbance, then any discrete physical theory is classical	Corsin Pfister	2012-12-04	Scientific Series	View details
Principle of relativity for quantum theory	Marco Zaopo	2012-11-20	Scientific Series	View details
Quasiprobability representations of qubits		2012-11-13	Scientific Series	View details
What's an unknown POVM, and what does a two qubit state look like?	Matthew Pusey	2012-11-06	Scientific Series	View details
What is a Wavefunction?	Wayne Myrvold	2012-11-01	Scientific Series	View details
Thermodynamics of correlated quantum systems and a generalized exchange fluctuation theorem.	David Jennings	2012-10-23	Scientific Series	View details
New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics	Tobias Fritz	2012-10-09	Scientific Series	View details

Quantum Foundations

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