Quantum Foundations

416 talks

S002

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Displaying 265 - 276 of 416

Quantum measurements constrained by symmetry

Leon Loveridge University of York
April 30, 2013

PIRSA:13040124
Quantum Foundations
The theory of composition in physics

Lucien Hardy Perimeter Institute for Theoretical Physics
April 16, 2013

PIRSA:13040121
Quantum Foundations
The Quantum Steering Ellipsoid

Sania Jevtic Imperial College London
March 26, 2013

PIRSA:13030112
Quantum Foundations
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

Quantum measurements constrained by symmetry

Leon Loveridge University of York
April 30, 2013

PIRSA:13040124
Quantum Foundations
The Wigner-Araki-Yanase (WAY) theorem delineates circumstances under which a class of quantum measurements is ruled out. Specifically, it states that any observable (given as a self adjoint operator) not commuting with an additive conserved quantity of a quantum system and measuring apparatus combined admits no repeatable measurements. I'll review the content of this theorem and present some new work which generalises and strengthens the existing results. The observation that the WAY constraint vanishes if the observable-to-be-measured is ``relativised'' (in a suitable sense) points to interesting links with quantum reference frames and superselection rules. I'll discuss some of these connections and raise some open questions.
The theory of composition in physics

Lucien Hardy Perimeter Institute for Theoretical Physics
April 16, 2013

PIRSA:13040121
Quantum Foundations
We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such regions joined together). We propose certain fundamental axioms which, it seems, should be satisfied in any theory of composition. A key axiom is the order independence axiom which says we can describe the composition of a composite object in any order. Then we provide a notation for describing composite objects that naturally leads to these axioms being satisfied. In any given physical context we are interested in the value of certain properties for the objects (such as whether the object is possible, what probability it has, how wide it is, and so on). We associate a generalized state with an object. This can be used to calculate the value of those properties we are interested in for for this object. We then propose a certain principle, the composition principle, which says that we can determine the generalized state of a composite object from the generalized states for the components by means of a calculation having the same structure as the description of the generalized state. The composition principle provides a link between description and prediction.
The Quantum Steering Ellipsoid

Sania Jevtic Imperial College London
March 26, 2013

PIRSA:13030112
Quantum Foundations
A quantum steering ellipsoid may be used to faithfully represent a density matrix ? describing two qubits A and B. The ellipsoid is the geometric set of states that Bob can steer Alice's qubit to when he implements all possible measurements on his qubit. We show how the correlations between qubits A and B manifest themselves in this paradigm, giving simple conditions for when the state is entangled, or has discord. We will also present novel features of the two qubit state that are revealed by the steering ellipsoid formalism, and show that a state corresponding to an ellipsoid with non-zero volume contains a new type of correlation.
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.

Title	Speaker(s)	Date	Talk Type	Info
Quantum measurements constrained by symmetry	Leon Loveridge	2013-04-30	Scientific Series	View details
The theory of composition in physics	Lucien Hardy	2013-04-16	Scientific Series	View details
The Quantum Steering Ellipsoid	Sania Jevtic	2013-03-26	Scientific Series	View details
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

Quantum Foundations

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