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 721 - 732 of 1183

A histories perpective on bounding quantum correlations

Joe Henson
BNP Paribas Asset Management London
March 18, 2014

PIRSA:14030111
Quantum Foundations
Seeing is Believing: Direct Observation of a General Quantum State

Jeff Lundeen
University of Ottawa
March 17, 2014

PIRSA:14030110
Quantum Foundations
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states

Matthew Leifer
Chapman University
February 18, 2014

PIRSA:14020145
Quantum Foundations
Does the Quantum Particle know its own Energy?

Rafael Sorkin
Perimeter Institute for Theoretical Physics
January 21, 2014

PIRSA:14010106
Quantum Foundations
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
Universal fault-tolerant quantum computation with only transversal gates and error correction

Adam Paetznick
September 25, 2013

PIRSA:13090069
Quantum Foundations

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.
Seeing is Believing: Direct Observation of a General Quantum State

Jeff Lundeen
University of Ottawa
March 17, 2014

PIRSA:14030110
Quantum Foundations
Central to quantum theory, the wavefunction is a complex distribution associated with a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of it through its use to calculate measurement outcome probabilities through the Born Rule. Tomographic methods can reconstruct the wavefunction from measured probabilities. In contrast, I present a method to directly measure the wavefunction so that its real and imaginary components appear straight on our measurement apparatus. I will also present new work extending this concept to mixed quantum states. This extension directly measures a little-known proposal by Dirac for a classical analog to a quantum operator. Furthermore, it reveals that our direct measurement is a rigorous example of a quasi-probability phase-space (i.e. x,p) distribution that is closely related to the Q, P, and Wigner functions. Our direct measurement method gives the quantum state a plain and general meaning in terms of a specific set of simple operations in the lab.
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states

Matthew Leifer
Chapman University
February 18, 2014

PIRSA:14020145
Quantum Foundations
The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (representing knowledge, information, or belief) or an ontic state (a direct reflection of reality)? In the ontological models framework, quantum states correspond to probability measures over more fundamental states of reality. The quantum state is then ontic if every pair of pure states corresponds to a pair of measures that do not overlap, and is otherwise epistemic. Recently, several authors have derived theorems that aim to show that the quantum state must be ontic in this framework. Each of these theorems involve auxiliary assumptions of varying degrees of plausibility. Without such assumptions, it has been shown that models exist in which the quantum state is epistemic. However, the definition of an epistemic quantum state used in these works is extremely permissive. Only two quantum states need correspond to overlapping measures and furthermore the amount of overlap may be arbitrarily small. In order to provide an explanation of quantum phenomena such as no-cloning and the indistinguishability of pure states, the amount of overlap should be comparable to the inner product of the quantum states. In this talk, I show, without making auxiliary assumptions, that the ratio of overlap to inner product must go to zero exponentially in Hilbert space dimension for some families of states. This is done by connecting the overlap to Kochen-Specker noncontextuality, from which we infer that any contextuality inequality gives a bound on the ratio of overlap to inner product.
Does the Quantum Particle know its own Energy?

Rafael Sorkin
Perimeter Institute for Theoretical Physics
January 21, 2014

PIRSA:14010106
Quantum Foundations
If a wave function does not describe microscopic reality then what does? Reformulating quantum mechanics in path-integral terms leads to a notion of ``precluded event" and thence to the proposal that quantal reality differs from classical reality in the same way as a set of worldlines differs from a single worldline. One can then ask, for example, which sets of electron trajectories correspond to a Hydrogen atom in its ground state and how they differ from those of an excited state. We address the analogous questions for simple model that replaces the electron by a particle hopping (in discrete time) on a circular lattice.
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.
Universal fault-tolerant quantum computation with only transversal gates and error correction

Adam Paetznick
September 25, 2013

PIRSA:13090069
Quantum Foundations
Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. It is known, however, that transversal gates alone cannot be computationally universal. I will show that the limitation on universality can be circumvented using only fault-tolerant error correction, which is already required anyway. This result applies to ``triorthogonal'' stabilizer codes, which were recently introduced by Bravyi and Haah for state distillation. I will show that triothogonal codes admit transversal implementation of the controlled-controlled-Z gate, and then demonstrate a transversal Hadamard construction which uses error correction to preserve the codespace. I will also discuss how to adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.

Title	Speaker(s)	Date	Talk Type	Info link
A histories perpective on bounding quantum correlations	Joe Henson	2014-03-18	Scientific Series	View details
Seeing is Believing: Direct Observation of a General Quantum State	Jeff Lundeen	2014-03-17	Scientific Series	View details
Psi-epistemic models are exponentially bad at explaining the distinguishability of quantum states	Matthew Leifer	2014-02-18	Scientific Series	View details
Does the Quantum Particle know its own Energy?	Rafael Sorkin	2014-01-21	Scientific Series	View details
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
Universal fault-tolerant quantum computation with only transversal gates and error correction	Adam Paetznick	2013-09-25	Scientific Series	View details

Quantum Foundations

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