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 733 - 744 of 1206

Space-Time Circuit-to-Hamiltonian construction and Its Applications

Barbara Terhal Delft University of Technology
July 23, 2014

PIRSA:14070031
Quantum Foundations
Inferring causal structure: a quantum advantage

Katja Ried Universität Innsbruck
July 17, 2014

PIRSA:14070021
Quantum Foundations
Local quanta, unitary inequivalence, and vacuum entanglement

Hans Westman
May 20, 2014

PIRSA:14050117
Quantum Foundations
Physics, Logic and Mathematics of Time

Louis Kauffman University of Illinois at Chicago
May 02, 2014

PIRSA:14050032
Quantum Foundations
Quantum thermalization and many-body Anderson localization

David Huse Princeton University
April 30, 2014

PIRSA:14040066
Quantum Foundations
Categories of Convex Sets and C*-Algebras

Robert Furber Radboud Universiteit Nijmegen
April 15, 2014

PIRSA:14040140
Quantum Foundations
A non-commuting stabilizer formalism

Xiaotong Ni Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 09, 2014

PIRSA:14040136
Quantum Foundations

Quantum Gravity
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
The invasion of physics by information theory

Robert Spekkens Perimeter Institute for Theoretical Physics
March 26, 2014

PIRSA:14030085
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

Space-Time Circuit-to-Hamiltonian construction and Its Applications

Barbara Terhal Delft University of Technology
July 23, 2014

PIRSA:14070031
Quantum Foundations
The circuit-to-Hamiltonian construction translates a dynamics (a quantum circuit and its output) into statics (the groundstate of a circuit Hamiltonian) by explicitly defining a quantum register for a clock. The standard Feynman-Kitaev construction uses one global clock for all qubits while we consider a different construction in which a clock is assigned to each point in space where a qubit of the quantum circuit resides. We show how one can apply this construction to one-dimensional quantum circuits for which the circuit Hamiltonian realizes the dynamics of a vibrating string. We discuss how the construction can be used (1) in quantum complexity theory to obtain new and stronger results in QMA and (2) how one can realize, based on this construction, universal quantum adiabatic computation and a universal quantum walk using a 2D interacting particle Hamiltonian. See http://arxiv.org/abs/1311.6101
Inferring causal structure: a quantum advantage

Katja Ried Universität Innsbruck
July 17, 2014

PIRSA:14070021
Quantum Foundations
A fundamental question in trying to understand the world -- be it classical or quantum -- is why things happen. We seek a causal account of events, and merely noting correlations between them does not provide a satisfactory answer. Classical statistics provides a better alternative: the framework of causal models proved itself a powerful tool for studying causal relations in a range of disciplines. We aim to adapt this formalism to allow for quantum variables and in the process discover a new perspective on how causality is different in the quantum world. Causal inference is a central task in the context of causal models: given observed statistics over a set of variables, one aims to infer how they are causally related. Yet in the seemingly simple case of just two classical variables, this is impossible (unless one makes additional assumptions). I will show how the analogous task for quantum variables can be solved. This quantum advantage is reminiscent of the advantages that quantum mechanics offers in computing and communication, and may lead to similarly rich insights. Our scheme is corroborated by data obtained in collaboration with Kevin Resch's experimental group. Time permitting, I will also address other applications of the quantum causal models. arXiv:1406.5036
Local quanta, unitary inequivalence, and vacuum entanglement

Hans Westman
May 20, 2014

PIRSA:14050117
Quantum Foundations
In this work we develop a formalism for describing localised quanta for a real-valued Klein-Gordon field in a one-dimensional box [0, R]. We quantise the field using non-stationary local modes which, at some arbitrarily chosen initial time, are completely localised within the left or the right side of the box. In this concrete set-up we directly face the problems inherent to a notion of local field excitations, usually thought of as elementary particles. Specifically, by computing the Bogoliubov coefficients relating local and standard (global) quantizations, we show that the local quantisation yields a Fock space F^L which is unitarily inequivalent to the standard one F^G. In spite of this, we find that the local creators and annihilators remain well defined in the global Fock space F^G, and so do the local number operators associated to the left and right partitions of the box. We end up with a useful mathematical toolbox to analyse and characterise local features of quantum states in F^G . Specifically, an analysis of the global vacuum state |0_G> ∈ F^G in terms of local number operators shows, as expected, the existence of entanglement between the left and right regions of the box. The local vacuum |0_L> ∈ F^L , on the contrary, has a very different character. It is neither cyclic nor separating and displays no entanglement. Further analysis shows that the global vacuum also exhibits a distribution of local excitations reminiscent, in some respects, of a thermal bath. We discuss how the mathematical tools developed herein may open new ways for the analysis of fundamental problems in local quantum field theory.
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.
Quantum thermalization and many-body Anderson localization

David Huse Princeton University
April 30, 2014

PIRSA:14040066
Quantum Foundations
Progress in physics and quantum information science motivates much recent study of the behavior of strongly-interacting many-body quantum systems fully isolated from their environment, and thus undergoing unitary time evolution. What does it mean for such a system to go to thermal equilibrium? I will explain the Eigenstate Thermalization Hypothesis (ETH), which posits that each individual exact eigenstate of the system's Hamiltonian is at thermal equilibrium, and which appears to be true for most (but not all) quantum many-body systems. Prominent among the systems that do not obey this hypothesis are quantum systems that are many-body Anderson localized and thus do not constitute a reservoir that can thermalize itself. When the ETH is true, one can do standard statistical mechanics using the `single-eigenstate ensembles', which are the limit of the microcanonical ensemble where the `energy window' contains only a single many-body quantum state. These eigenstate ensembles are more powerful than the traditional statistical mechanical ensembles, in that they can also "see" the quantum phase transition in to the localized phase, as well as a rich new world of phases and phase transitions within the localized phase.
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.
A non-commuting stabilizer formalism

Xiaotong Ni Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 09, 2014

PIRSA:14040136
Quantum Foundations

Quantum Gravity
We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of single-qubit operators drawn from the group {\alpha I, X,S}, where \alpha=e^{i\pi/4} and S=diag(1,i). We provide techniques to efficiently compute various properties, related to e.g. bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians etc. We also highlight significant differences compared to the Pauli stabilizer formalism. In particular we give examples of states in our formalism which cannot arise in the Pauli stabilizer formalism, such as topological models that supports non-abelian anyons. This is a joint work with O. Buerschaper and M. van den Nest.
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.
The invasion of physics by information theory

Robert Spekkens Perimeter Institute for Theoretical Physics
March 26, 2014

PIRSA:14030085
Quantum Foundations
When we think of a revolution in physics, we usually think of a physical theory that manages to overthrow its predecessor. There is another kind of revolution, however, that typically happens more slowly but that is often the key to achieving the first sort: it is the discovery of a novel perspective on an existing physical theory. The use of least-action principles, symmetry principles, and thermodynamic principles are good historical examples. It turns out that we can refine our understanding of many of these principles by characterizing certain properties of physical states as resources. I will discuss some of the highlights of two resource theories: the resource theory of asymmetry, which characterizes the relations among quantum states that break a symmetry; and the resource theory of athermality, which characterizes the relations among quantum states that deviate from thermal equilibrium. In particular, I will discuss how Noether's theorem does not capture all of the consequences of symmetries of the dynamics, and how the second law of thermodynamics does not capture all of the constraints on thermodynamic transitions. Finally, I will show that both asymmetry and athermality are informational resources, and that rehabilitated versions of Noether's theorem and the second law can both be understood as constraints on data processing. Considerations such as these---as well as evidence from other fronts of the invasion---make a compelling case for the revolutionary cause of reconceiving physics from an information-theoretic perspective.
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.

Title	Speaker(s)	Date	Talk Type	Info link
Space-Time Circuit-to-Hamiltonian construction and Its Applications	Barbara Terhal	2014-07-23	Scientific Series	View details
Inferring causal structure: a quantum advantage	Katja Ried	2014-07-17	Scientific Series	View details
Local quanta, unitary inequivalence, and vacuum entanglement	Hans Westman	2014-05-20	Scientific Series	View details
Physics, Logic and Mathematics of Time	Louis Kauffman	2014-05-02	Scientific Series	View details
Quantum thermalization and many-body Anderson localization	David Huse	2014-04-30	Scientific Series	View details
Categories of Convex Sets and C*-Algebras	Robert Furber	2014-04-15	Scientific Series	View details
A non-commuting stabilizer formalism	Xiaotong Ni	2014-04-09	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
The invasion of physics by information theory	Robert Spekkens	2014-03-26	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

Quantum Foundations

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