Quantum Foundations

408 talks

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Quantum Foundations

Displaying 241 - 252 of 408

Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.

Ravi Kunjwal
Funds for Scientific Research - FNRS
January 14, 2014

PIRSA:14010102
Quantum Foundations
Rebuilding Mathematics on a Quantum Logical Foundation

Richard deJonghe
University of Illinois at Chicago
December 10, 2013

PIRSA:13120060
Quantum Foundations
Quantum Mechanics as Classical Physics

Charles Sebens
University of Michigan–Ann Arbor
December 03, 2013

PIRSA:13120006
Quantum Foundations
Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States

Elie Wolfe
Perimeter Institute for Theoretical Physics
November 26, 2013

PIRSA:13110092
Quantum Foundations
Quantum mechanics as an operationally time symmetric probabilistic theory

Ognyan Oreshkov
Université Libre de Bruxelles
November 12, 2013

PIRSA:13110057
Quantum Foundations
A note on emergent classical behavior and approximations to decoherence functionals

Henrique Gomes
University of Oxford
November 05, 2013

PIRSA:13110085
Quantum Foundations
Can ‘sub-quantum’ theories based on a background field escape Bell’s no-go theorem ?

Louis Vervoort
Université de Montréal
October 15, 2013

PIRSA:13100085
Quantum Foundations
Coalgebras, Models and Logics for Quantum Systems
September 17, 2013

PIRSA:13090072
Quantum Foundations
Quantum States are Consistent Probability Distributions

Nadish de Silva
University of Oxford
September 12, 2013

PIRSA:13090070
Quantum Foundations
Quantum Observables as Real-valued Functions and Quantum Probability
September 10, 2013

PIRSA:13090068
Quantum Foundations
A Non-Local Reality: Is there a Phase Uncertainty in Quantum Mechanics?
- Niayesh Afshordi
  University of Waterloo
- Elizabeth Gould
  Arthur B. McDonald Canadian Astroparticle Physics Research Institute
September 03, 2013

PIRSA:13090064
Quantum Foundations
Can Quantum correlations be Explained Casually

Robert Spekkens
Perimeter Institute for Theoretical Physics

July 15, 2013

PIRSA:13070030

Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.

Ravi Kunjwal
Funds for Scientific Research - FNRS
January 14, 2014

PIRSA:14010102
Quantum Foundations
The purpose of this talk is twofold: First, following Spekkens, to motivate noncontextuality as a natural principle one might expect to hold in nature and introduce operational noncontextuality inequalities motivated by a contextuality scenario first considered by Ernst Specker. These inequalities do not rely on the assumption of outcome-determinism which is implicit in the usual Kochen-Specker (KS) inequalities. We argue that they are the appropriate generalization of KS inequalities, serving as a test for the possibility of noncontextual explanations of experimental data. This is very much in the spirit of Bell inequalities, which provide theory-independent tests for local hidden variable explanations of experimental data without relying on the assumption of outcome-determinism. The second purpose is to point out a curious feature of quantum theory, motivated by the connections between (in)compatibility and (non)contextuality: namely, that it admits all conceivable (in)compatibility relations between observables.
Rebuilding Mathematics on a Quantum Logical Foundation

Richard deJonghe
University of Illinois at Chicago
December 10, 2013

PIRSA:13120060
Quantum Foundations
It is not unnatural to expect that difficulties lying at the foundations of quantum mechanics can only be resolved by literally going back and rethinking the quantum theory from first principles (namely, the principles of logic). In this talk, I will present a first-order quantum logic which generalizes the propositional quatum logic originated by Birkhoff and von Neumann as well as the standard classical predicate logic used in the development of virtually all of modern mathematics. I will then use this quantum logic to begin to build the foundations of a new ``quantum mathematics'' --- in particular a quantum set theory and a quantum arithmetic --- which has the potential to provide a completely new mathematical framework in which to develop the theory of quantum
mechanics.
Quantum Mechanics as Classical Physics

Charles Sebens
University of Michigan–Ann Arbor
December 03, 2013

PIRSA:13120006
Quantum Foundations
On the face of it, quantum physics is nothing like classical physics. Despite its oddity, work in the foundations of quantum theory has provided some palatable ways of understanding this strange quantum realm. Most of our best theories take that story to include the existence of a very non-classical entity: the wave function. Here I offer an alternative which combines elements of Bohmian mechanics and the many-worlds interpretation to form a theory in which there is no wave function. According to this theory, all there is at the fundamental level are particles interacting via Newtonian forces. In this sense, the theory is classical. However, it is still undeniably strange as it posits the existence of many worlds. Unlike the many worlds of the many-worlds interpretation, these worlds are fundamental, not emergent, and are interacting, not causally isolated. The theory will be presented as a fusion of the many-worlds interpretation and Bohmian mechanics, but can also be seen as a foundationally clear version of quantum hydrodynamics. A key strength of this theory is that it provides a simple and compelling story about the connection between the amplitude-squared of the wave function and probability. The theory also gives a natural explanation of the way the wave function transforms under time reversal and Galilean boosts.
Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States

Elie Wolfe
Perimeter Institute for Theoretical Physics
November 26, 2013

PIRSA:13110092
Quantum Foundations
We present a method for determining the maximum possible violation of any linear Bell inequality per quantum mechanics. Essentially this amounts to a constrained optimization problem for an observable’s eigenvalues, but the problem can be reformulated so as to be analytically tractable. This opens the door for an arbitrarily precise characterization of quantum correlations, including allowing for non-random marginal expectation values. Such a characterization is critical when contrasting QM to superficially similar general probabilistic theories. We use such marginal-involving quantum bounds to estimate the volume of all possible quantum statistics in the complete 8-dimensional probability space of the Bell-CHSH scenario, measured relative to both local hidden variable models as well as general no-signaling theories. See arXiv:1106.2169. Time permitting, we’ll also discuss how one might go about trying to prove that a given mixed state is, in fact, not entangled. (The converse problem of certifying non-zero entanglement has received extensive treatment already.) Instead of directly asking if any separable representation exists for the state, we suggest simply checking to see if it “fits” some particular known-separable form. We demonstrate how a surprisingly valuable sufficient separability criterion follows merely from considering a highly-generic separable form. The criterion we generate for diagonally-symmetric mixed states is apparently completely tight, necessary and sufficient. We use integration to quantify the “volume” of states captured by our criterion, and show that it is as large as the volume of states associated with the PPT criterion; this simultaneously proves our criterion to be necessary as well as the PPT criterion to be sufficient, on this family of states. The utility of a sufficient separability criterion is evidenced by categorically rejecting Dicke-model superradiance for entanglement generation schema. See arXiv:1307.5779.
Quantum mechanics as an operationally time symmetric probabilistic theory

Ognyan Oreshkov
Université Libre de Bruxelles
November 12, 2013

PIRSA:13110057
Quantum Foundations
The standard formulation of quantum mechanics is operationally asymmetric with respect to time reversal---in the language of compositions of tests, tests in the past can influence the outcomes of test in the future but not the other way around. The question of whether this represents a fundamental asymmetry or it is an artifact of the formulation is not a new one, but even though various arguments in favor of an inherent symmetry have been made, no complete time-symmetric formulation expressed in rigorous operational terms has been proposed. Here, we discuss such a possible formulation based on a generalization of the usual notion of test. We propose to regard as a test any set of events between an input and an output system which can be obtained by an autonomously defined laboratory procedure. This includes standard tests, as well as proper subsets of the complete set of outcomes of standard tests, whose realization may require post-selection in addition to pre-selection. In this approach, tests are not expected to be operations that are up to the choices of agents---the theory simply says what circuits of tests may occur and what the probabilities for their outcomes would be, given that they occur. By virtue of the definition of test, the probabilities for the outcomes of past tests can depend on tests that take place in the future. Such theories have been previously called non-causal, but here we revisit that notion of causality. Using the Choi-Jamiolkowski isomorphism, every test in that formulation, commonly regarded as inducing transformations from an input to an output system, becomes equivalent to a passive detection measurement applied jointly on two input systems---one from the past and one from the future. This is closely related to the two-state vector formalism, but it comes with a conceptual revision: every measurement is a joint measurement on two separate systems and not on one system described by states in the usual Hilbert space and its dual. We thus obtain a static picture of quantum mechanics in space-time or more general structures, in which every experiment is a local measurement on a global quantum state that generalizes the recently proposed quantum process matrix. The existence of two types of systems in the proposed formalism allows us to define causation in terms of correlations without invoking the idea of intervention, offering a possible answer to the problem of the meaning of causation. The framework is naturally compatible with closed time-like curves and other exotic causal structures.
A note on emergent classical behavior and approximations to decoherence functionals

Henrique Gomes
University of Oxford
November 05, 2013

PIRSA:13110085
Quantum Foundations
Although it can only be argued to have become consequential in the study of quantum cosmology, the question ``Why do we observe a classical world? " has been one of the biggest preoccupations of quantum foundations. In the consistent histories formalism, the question is shifted to an analysis of the telltale sign of quantum mechanics: superposition of states. In the consistent histories formalism, histories of the system which ``decohere", i.e. fall out of superposition or have negligible interference can be subjected to a notion of classical probability. In this paper we use an extension of Kirchoff's diffraction formula for wave functions on configuration spaces to give a different analysis and an approximation of decoherence. The Kirchoff diffraction formula lies conveniently at the midway between path integrals, wave equations, and classical behavior. By using it, we formulate an approximate dampening of the amplitude of superposition of histories. The dampening acts on each middle element of the fine-grained history {c_\alpha}, and is a function of the angle formed between {c_{n-1},c_n} and {c_n,c_{n+1}}, as classical trajectories in configuration space. As an example we apply the formalism to a modified gravity theory in the ADM gravitational conformal superspace.
Can ‘sub-quantum’ theories based on a background field escape Bell’s no-go theorem ?

Louis Vervoort
Université de Montréal
October 15, 2013

PIRSA:13100085
Quantum Foundations
In systems described by Ising-like Hamiltonians, such as spin-lattices, the Bell Inequality can be strongly violated. Surprisingly, these systems are both local and non-superdeterministic. They are local, because 1) they include only local, near-neighbor interaction, 2) they satisfy, accordingly, the Clauser-Horne factorability condition, and 3) they can violate the Bell Inequality also in dynamic Bell experiments. Starting from this result we construct an elementary hidden-variable model, based on a generalized Ising Hamiltonian, describing the interaction of the Bell-particles with a stochastic ‘background’ medium. We suggest that such a model is a simple version of a variety of recently developed ‘sub-quantum’ theories, by authors as Nelson, Adler, De la Pena, Cetto, Groessing, Khrennikov, all based on a background field. We investigate how the model might be turned into a realistic theory. Finally, it appears that background-based models can be tested and discriminated from quantum mechanics by a straightforward extension of existing experiments.
Coalgebras, Models and Logics for Quantum Systems
September 17, 2013

PIRSA:13090072
Quantum Foundations
Coalgebras are a flexible tool commonly used in computer science to model abstract devices and systems. Coalgebraic models also come with a natural notion of logics for the systems being modelled. In this talk we will introduce coalgebras and aim to illustrate their usefulness for modelling physical systems. Extending earlier work of Abramsky, we will show how a weakening of the usual morphisms for coalgebras provides the flexibility to model quantum systems in an easy to motivate manner. We will then investigate how a natural extension to the usual notion of coalgebraic logic can be used to produce logics for reasoning about quantum systems and protocols. No prior knowledge of coalgebras will be assumed for this talk, and the emphasis throughout will be on examples rather than technical details.
Quantum States are Consistent Probability Distributions

Nadish de Silva
University of Oxford
September 12, 2013

PIRSA:13090070
Quantum Foundations
We describe a notion of state for a quantum system which is given in terms of a collection of empirically realizable probability distributions and is formally analogous to the familiar concept of state from classical statistical mechanics. We first demonstrate the mathematical equivalence of this new notion to the standard quantum notion of density matrix. We identify the simple logical consistency condition (a generalization of the familiar no-signalling condition) which a collection of distributions must obey in order to reconstruct the unique quantum state from which they arise. In this way, we achieve a formal expression of the common intuition of a quantum state as being classical distributions on compatible observables.
Quantum Observables as Real-valued Functions and Quantum Probability
September 10, 2013

PIRSA:13090068
Quantum Foundations
Quantum observables are commonly described by self-adjoint operators on a Hilbert space H. I will show that one can equivalently describe observables by real-valued functions on the set P(H) of projections, which we call q-observable functions. If one regards a quantum observable as a random variable, the corresponding q-observable function can be understood as a quantum quantile function, generalising the classical notion. I will briefly sketch how q-observable functions relate to the topos approach to quantum theory and the process called daseinisation. The topos approach provides a generalised state space for quantum systems that serves as a joint sample space for all quantum observables. This is joint work with Barry Dewitt.
A Non-Local Reality: Is there a Phase Uncertainty in Quantum Mechanics?
- Niayesh Afshordi
  University of Waterloo
- Elizabeth Gould
  Arthur B. McDonald Canadian Astroparticle Physics Research Institute
September 03, 2013

PIRSA:13090064
Quantum Foundations
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of
relativistic locality include the Bell's inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava-Lifshitz gravity. Here, we explore a recent proposal for a ``real ensemble'' non-local description of quantum mechanics, in which ``particles'' can copy each others' observables AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has (ordinary) quantum mechanics as a fixed point, where all particles with the same observables have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems (in our study) are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per observable, as well as systematic deviations from quantum mechanics, decay as ~ (EnergyXTime)^{-n}, where n > 2. Interestingly, this convergence is controlled by the absolute value of energy (and not energy difference). Finally, we discuss different issues related to this theory, as well as potential implications for early universe, and the cosmological constant problem.
Can Quantum correlations be Explained Casually

Robert Spekkens
Perimeter Institute for Theoretical Physics

July 15, 2013

PIRSA:13070030

Title	Speaker(s)	Date	Talk Type	Info
Noncontextuality without determinism and admissible (in)compatibility relations: revisiting Specker's parable.	Ravi Kunjwal	2014-01-14	Scientific Series	View details
Rebuilding Mathematics on a Quantum Logical Foundation	Richard deJonghe	2013-12-10	Scientific Series	View details
Quantum Mechanics as Classical Physics	Charles Sebens	2013-12-03	Scientific Series	View details
Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States	Elie Wolfe	2013-11-26	Scientific Series	View details
Quantum mechanics as an operationally time symmetric probabilistic theory	Ognyan Oreshkov	2013-11-12	Scientific Series	View details
A note on emergent classical behavior and approximations to decoherence functionals	Henrique Gomes	2013-11-05	Scientific Series	View details
Can ‘sub-quantum’ theories based on a background field escape Bell’s no-go theorem ?	Louis Vervoort	2013-10-15	Scientific Series	View details
Coalgebras, Models and Logics for Quantum Systems		2013-09-17	Scientific Series	View details
Quantum States are Consistent Probability Distributions	Nadish de Silva	2013-09-12	Scientific Series	View details
Quantum Observables as Real-valued Functions and Quantum Probability		2013-09-10	Scientific Series	View details
A Non-Local Reality: Is there a Phase Uncertainty in Quantum Mechanics?	Niayesh Afshordi, Elizabeth Gould	2013-09-03	Scientific Series	View details
Can Quantum correlations be Explained Casually	Robert Spekkens	2013-07-15		View details

Quantum Foundations

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