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Algebraic characterization of entanglement classes

Markus Grassl Max Planck Institute for the Science of Light
September 19, 2014

PIRSA:14090070
Quantum Physics
Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
September 19, 2014

PIRSA:14090072
High Energy Physics

Condensed Matter

General Relativity & Quantum Cosmology
14/15 PSI Quantum Theory-10

Joseph Emerson Institute for Quantum Computing (IQC)

September 19, 2014

PIRSA:14090053
14/15 PSI - Relativity- Lecture 10

Neil Turok University of Edinburgh

September 19, 2014

PIRSA:14090022
Observables and Change in Totally Constrained Systems

Karim Thebault Ludwig-Maximilians-Universität München (LMU)
September 18, 2014

PIRSA:14090004
General Relativity & Quantum Cosmology
Evolution of quantum field, particle content, and classicality in the three stage universe

Suprit Singh IUCAA - The Inter-University Centre for Astronomy and Astrophysics
September 18, 2014

PIRSA:14090082
Astrophysics
14/15 PSI Quantum Theory-9

Agata Branczyk IBM (Canada)

September 18, 2014

PIRSA:14090052
14/15 PSI - Relativity- Lecture 9

Neil Turok University of Edinburgh

September 18, 2014

PIRSA:14090021
A magic bullet for numerous quantum-informational tasks

Mark Howard University of Waterloo

September 17, 2014

PIRSA:14090006
Boltzmann's Dog and Darwin's Finch: The statistical thermodynamics of self-replication and evolution

Jeremy England Massachusetts Institute of Technology (MIT)

September 17, 2014

PIRSA:14090003
14/15 PSI Quantum Theory-8

Joseph Emerson Institute for Quantum Computing (IQC)

September 17, 2014

PIRSA:14090051
Irreversibility, Entropy Production, and and Self-organization far from Equilibrium

Jeremy England Massachusetts Institute of Technology (MIT)
September 17, 2014

PIRSA:14090073
Condensed Matter

Algebraic characterization of entanglement classes

Markus Grassl Max Planck Institute for the Science of Light
September 19, 2014

PIRSA:14090070
Quantum Physics
Entanglement is a key feature of composite quantum system which is directly related to the potential power of quantum computers. In most computational models, it is assumed that local operations are relatively easy to implement. Therefore, quantum states that are related by local operations form a single entanglement class. In the case of local unitary operations, a finite set of polynomial invariants provides a complete characterization of the entanglement classes. Unfortunately, one faces the problem of combinatorial explosion so that computing such a complete set of invariants becomes difficult already for quite small system. The two main problems in this context are to compute invariants and to decide completeness, i.e., whether a given set of invariants generates the full invariant ring. Important tools are both univariate and multivariate Hilbert series which are already difficult to compute. We will also address computational aspects of these problems and techniques for showing completeness of a set of invariants.
Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
September 19, 2014

PIRSA:14090072
High Energy Physics

Condensed Matter

General Relativity & Quantum Cosmology
We discuss properties of 2-point functions in CFTs in 2+1D at finite temperature. For concreteness, we focus on those involving conserved flavour currents, in particular on the associated conductivity. At frequencies much greater than the temperature, ω >> T, the ω dependence of the conductivity can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these large ω results to the corresponding correlators of holographic representations of the CFT: the holographic approach then allows us to extrapolate to small ω/T. Other holographic studies implicitly only used the OPE between the currents and the energy-momentum tensor, and this yields the correct leading large ω behavior for a large class of CFTs. However, for the Wilson-Fisher CFT a relevant “thermal” operator must also be considered, and then consistency with the Monte Carlo results is obtained without a previously needed ad hoc rescaling of the T value [1]. We also use the OPE to prove sum rules obeyed by the conductivity. **In collaboration with A. Katz, S. Sachdev and E. Sørensen** [1] WWK, E. Sørensen, S. Sachdev, Nat. Phys. 10, 361 (2014)
14/15 PSI Quantum Theory-10

Joseph Emerson Institute for Quantum Computing (IQC)

September 19, 2014

PIRSA:14090053
14/15 PSI - Relativity- Lecture 10

Neil Turok University of Edinburgh

September 19, 2014

PIRSA:14090022
Observables and Change in Totally Constrained Systems

Karim Thebault Ludwig-Maximilians-Universität München (LMU)
September 18, 2014

PIRSA:14090004
General Relativity & Quantum Cosmology
We isolate an important physical distinction between gauge symmetries which exist at the level of histories and states, and those which exist at the level of histories and not states. This distinction is characterised explicitly using a generalized Hamilton-Jacobi formalism within which a non-standard prescription for the observables of classical totally constrained systems is developed. These ideas motivate a `relational quantization' procedure which is different from the standard `Dirac quanization'. In particular, relational quantization of totally constrained systems leads to a formalism with superpositions of energy eigenstates and an enlarged set of quantum observables. These `Kucha\v{r} observables' can change independently of each other, and thus are associated with measurable quantities in excess of the `perennials' of the standard Dirac approach.
Evolution of quantum field, particle content, and classicality in the three stage universe

Suprit Singh IUCAA - The Inter-University Centre for Astronomy and Astrophysics
September 18, 2014

PIRSA:14090082
Astrophysics
I will discuss the evolution of a quantum scalar field in a toy universe which has three stages of evolution, viz., (i) an early (inflationary) de Sitter phase (ii) radiation-dominated phase and (iii) late-time (cosmological constant dominated) de Sitter phase. Using the Schr\"odinger picture, the scalar field equations are solved separately for the three stages and matched at the transition points. The boundary conditions are chosen so that field modes in the early de Sitter phase evolve from the Bunch-Davies vacuum state. I shall look the (time-dependent) particle content of this quantum state for the entire evolution of the universe and describe the various features both numerically and analytically. I shall also describe the quantum to classical transition in terms of a classicality parameter which tracks the particle creation and its effect on phase space correlation of the quantum field.
14/15 PSI Quantum Theory-9

Agata Branczyk IBM (Canada)

September 18, 2014

PIRSA:14090052
14/15 PSI - Relativity- Lecture 9

Neil Turok University of Edinburgh

September 18, 2014

PIRSA:14090021
A magic bullet for numerous quantum-informational tasks

Mark Howard University of Waterloo

September 17, 2014

PIRSA:14090006

A class of d-level quantum states called "magic states", whose initial purpose was to enable universal fault-tolerant computation within error-correcting codes, has a surprisingly broad range of applications. We begin by describing their structure with respect to the Clifford hierarchy, and in terms of convex geometry before proceeding to their applications. They appear to have some relevance to the search for SIC-POVMs in certain prime dimensions. A version of the CHSH non-local game, using a d-ary alphabet and Pauli measurements, has an optimal quantum strategy using magic states. Finally, magic states exhibit nice symmetries (balanced, minimum uncertainty) with respect to Pauli measurements and consequently could find applications in areas like cryptography.
Boltzmann's Dog and Darwin's Finch: The statistical thermodynamics of self-replication and evolution

Jeremy England Massachusetts Institute of Technology (MIT)

September 17, 2014

PIRSA:14090003

Living things operate according to well-known physical laws, yet it is challenging to discern specific, non-trivial consequences of these constraints for how an organism that is a product of evolution must behave. Part of the difficulty here is that life lives very far from thermal equilibrium, where many of our traditional theoretical tools fail us. However, recent developments in nonequilibrium statistical mechanics may help light a way forward. The goal of this talk will be to explain some of these developments, and show how they begin to offer a new perspective on the physics of self-replication, natural selection, and evolution.
14/15 PSI Quantum Theory-8

Joseph Emerson Institute for Quantum Computing (IQC)

September 17, 2014

PIRSA:14090051
Irreversibility, Entropy Production, and and Self-organization far from Equilibrium

Jeremy England Massachusetts Institute of Technology (MIT)
September 17, 2014

PIRSA:14090073
Condensed Matter
In the last few decades, substantial advances have been made in our ability to make general statements about the thermodynamics of systems driven far from thermal equilibrium. In this talk, I will give a brief overview of some the most basic results in this area and explain their connection to classic results in linear response theory. I will then describe how to formally construct the generalization of free energy for macrostates in a far-from-equilibrium system and discuss possible connections to self-organization phenomena in both biological and other contexts.

Title	Date	Collection	Type	Info
Algebraic characterization of entanglement classes	2014‑09‑19	Perimeter Institute Quantum Discussions	Scientific Series	View details
Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography	2014‑09‑19	Quantum Matter	Scientific Series	View details
14/15 PSI Quantum Theory-10	2014‑09‑19	14/15 PSI - Quantum Theory	Course	View details
14/15 PSI - Relativity- Lecture 10	2014‑09‑19	14/15 PSI -Relativity	Course	View details
Observables and Change in Totally Constrained Systems	2014‑09‑18	Quantum Gravity	Scientific Series	View details
Evolution of quantum field, particle content, and classicality in the three stage universe	2014‑09‑18	Cosmology and Gravitation	Scientific Series	View details
14/15 PSI Quantum Theory-9	2014‑09‑18	14/15 PSI - Quantum Theory	Course	View details
14/15 PSI - Relativity- Lecture 9	2014‑09‑18	14/15 PSI -Relativity	Course	View details
A magic bullet for numerous quantum-informational tasks	2014‑09‑17	Perimeter Institute Quantum Discussions	Scientific Series	View details
Boltzmann's Dog and Darwin's Finch: The statistical thermodynamics of self-replication and evolution	2014‑09‑17	Colloquium	Scientific Series	View details
14/15 PSI Quantum Theory-8	2014‑09‑17	14/15 PSI - Quantum Theory	Course	View details
Irreversibility, Entropy Production, and and Self-organization far from Equilibrium	2014‑09‑17	Quantum Matter	Scientific Series	View details

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Format results

Algebraic characterization of entanglement classes

Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography

14/15 PSI Quantum Theory-10

14/15 PSI - Relativity- Lecture 10

Observables and Change in Totally Constrained Systems

Evolution of quantum field, particle content, and classicality in the three stage universe

14/15 PSI Quantum Theory-9

14/15 PSI - Relativity- Lecture 9

A magic bullet for numerous quantum-informational tasks

Boltzmann's Dog and Darwin's Finch: The statistical thermodynamics of self-replication and evolution

14/15 PSI Quantum Theory-8

Irreversibility, Entropy Production, and and Self-organization far from Equilibrium

Algebraic characterization of entanglement classes

Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography

14/15 PSI Quantum Theory-10

14/15 PSI - Relativity- Lecture 10

Observables and Change in Totally Constrained Systems

Evolution of quantum field, particle content, and classicality in the three stage universe

14/15 PSI Quantum Theory-9

14/15 PSI - Relativity- Lecture 9

A magic bullet for numerous quantum-informational tasks

Boltzmann's Dog and Darwin's Finch: The statistical thermodynamics of self-replication and evolution

14/15 PSI Quantum Theory-8

Irreversibility, Entropy Production, and and Self-organization far from Equilibrium