Quantum Foundations

Quantum foundations concerns the conceptual and mathematical underpinnings of quantum theory. In particular, we search for novel quantum effects, consider how to interpret the formalism, ask where the formalism comes from, and how we might modify it. Research at Perimeter Institute is particularly concerned with reconstructing quantum theory from more natural postulates and reformulating the theory in ways that elucidate its conceptual structure. Research in the foundations of quantum theory naturally interfaces with research in quantum information and quantum gravity.

Displaying 757 - 768 of 1197

Completing Canonical Quantization

John Klauder University of Florida
May 21, 2013

PIRSA:13050006
Quantum Foundations
From Pauli's Principle to Fermionic Entanglement

Matthias Christandl ETH Zurich
May 03, 2013

PIRSA:13050005
Quantum Information

Quantum Foundations
Quantum measurements constrained by symmetry

Leon Loveridge University of York
April 30, 2013

PIRSA:13040124
Quantum Foundations
Laws of thermodynamics beyond the von Neumann regime

Oscar Dahlsten City University of Hong Kong
April 29, 2013

PIRSA:13040112
Quantum Foundations
The continuum limit of tensor networks: a path integral representation

David Jennings Imperial College London
April 22, 2013

PIRSA:13040113
Quantum Foundations
The theory of composition in physics

Lucien Hardy Perimeter Institute for Theoretical Physics
April 16, 2013

PIRSA:13040121
Quantum Foundations
Classical and quantum circuit obfuscation with braids

Stephen Jordan National Institute of Standards and Technology
April 08, 2013

PIRSA:13040111
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

Completing Canonical Quantization

John Klauder University of Florida
May 21, 2013

PIRSA:13050006
Quantum Foundations
The process of canonical quantization:is reexamined with the goal of ensuring there is only one reality, where $\hbar>0$, in which classical and quantum theories coexist. Two results are a clarification of the effect of canonical coordinate transformations and the role of Cartesian coordinates. Other results provide validation of alternative quantum procedures that allow acceptable solutions for models that exhibit unacceptable solutions using traditional procedures. Several examples will illustrate advantages of the new classical/quantum connection including one case where conventional methods lead to quantum triviality while the enhanced procedures lead to an acceptable nonlinear quantum behaviour. This seminar uses only simple physical and mathematical concepts, and should be widely accessible.
From Pauli's Principle to Fermionic Entanglement

Matthias Christandl ETH Zurich
May 03, 2013

PIRSA:13050005
Quantum Information

Quantum Foundations
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected for decades, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Surprisingly, these constraints are linear: they cut out a geometric object known as a polytope. This is a beautiful mathematical result, but are there systems whose physics is governed by these constraints? In order to address this question, we studied a system of a few fermions connected by springs. As we varied the spring constant, the occupation numbers moved within the polytope. The path they traced hugs very close to the boundary of the polytope, suggesting that the generalized constraints affect the system. I will mention the implications of these findings for the structure of few-fermion ground states and then discuss the relation between the geometry of the polytope and different types of fermionic entanglement.
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.
Laws of thermodynamics beyond the von Neumann regime

Oscar Dahlsten City University of Hong Kong
April 29, 2013

PIRSA:13040112
Quantum Foundations
A recent development in information theory is the generalisation of quantum Shannon information theory to the operationally motivated smooth entropy information theory, which originates in quantum cryptography research. In a series of papers the first steps have been taken towards creating a statistical mechanics based on smooth entropy information theory. This approach turns out to allow us to answer questions one might not have thought were possible in statistical mechanics, such as how much work one can extract in a given realisation, as a function of the failure-probability. This is in contrast to the standard approach which makes statements about average work. Here we formulate the laws of thermodynamics that this new approach gives rise to. We show in particular that the Second Law needs to be tightened. The new laws are motivated by our main quantitative result which states how much work one can extract or must invest in order to affect a given state change with a given probability of success. For systems composed of very large numbers of identical and uncorrelated subsystems, which we call the von Neumann regime, we recover the standard von Neumann entropy statements.

Joint work with Egloff, Renner and Vedral

http://arxiv.org/abs/1207.0434
The continuum limit of tensor networks: a path integral representation

David Jennings Imperial College London
April 22, 2013

PIRSA:13040113
Quantum Foundations
I will discuss a path-integral representation of continuum tensor networks that extends the continuous MPS class for 1-D quantum fields to arbitrary spatial dimensions while encoding desirable symmetries. The physical states can be interpreted as arising through a continuous measurement process by a lower dimensional virtual field with Lorentz symmetry. The resultant physical states naturally obey entropy area laws, with the expectation values of observables determined by the dissipative dynamics of the boundary field. The class offers the prospect of powerful new analytical and computational tools to describe the physics of strongly interacting field systems.
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.
Classical and quantum circuit obfuscation with braids

Stephen Jordan National Institute of Standards and Technology
April 08, 2013

PIRSA:13040111
Quantum Foundations
A circuit obfuscator is an algorithm that translates logic circuits into functionally-equivalent similarly-sized logic circuits that are hard to understand. While ad hoc obfuscators have been implemented, theoretical progress has mainly been limited to no-go results. In this work, we propose a new notion of circuit obfuscation, which we call partial indistinguishability. We then prove that, in contrast to previous definitions of obfuscation, partial indistinguishability obfuscation can be achieved by a polynomial-time algorithm. Specifically, our algorithm re-compiles the given circuit using a gate that satisfies the relations of the braid group, and then reduces to a braid normal form. Variants of our obfuscation algorithm can be applied to both classical and quantum circuits.
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

Title	Speaker(s)	Date	Talk Type	Info link
Completing Canonical Quantization	John Klauder	2013-05-21	Scientific Series	View details
From Pauli's Principle to Fermionic Entanglement	Matthias Christandl	2013-05-03	Scientific Series	View details
Quantum measurements constrained by symmetry	Leon Loveridge	2013-04-30	Scientific Series	View details
Laws of thermodynamics beyond the von Neumann regime	Oscar Dahlsten	2013-04-29	Scientific Series	View details
The continuum limit of tensor networks: a path integral representation	David Jennings	2013-04-22	Scientific Series	View details
The theory of composition in physics	Lucien Hardy	2013-04-16	Scientific Series	View details
Classical and quantum circuit obfuscation with braids	Stephen Jordan	2013-04-08	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 Foundations

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