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 769 - 780 of 1206

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 & 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
Exotic topological order from quantum fractal code

Beni Yoshida Perimeter Institute for Theoretical Physics
January 14, 2013

PIRSA:13010101
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

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 & 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
Exotic topological order from quantum fractal code

Beni Yoshida Perimeter Institute for Theoretical Physics
January 14, 2013

PIRSA:13010101
Quantum Foundations
We present a family of three-dimensional local quantum codes with pairs of fractal logical operators. It has two polynomials over finite fields as input parameters which generate fractal shapes of anti-commuting logical operators, and possesses exotic topological order with quantum glassiness which is beyond descriptions of conventional topological field theory. A necessary and sufficient condition for being free from string-like logical operators is obtained under which the model works as marginally self-correcting quantum memory. We also provide theoretical tools to analyze physical and coding properties of translation symmetric stabilizer Hamiltonians.
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.

Title	Speaker(s)	Date	Talk Type	Info link
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
Exotic topological order from quantum fractal code	Beni Yoshida	2013-01-14	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

Quantum Foundations

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