The Quantum Landscape 2013

Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory
May 30, 2013

PIRSA:13050070
Mathematical physics
Generalizations of Quantum Theory
- Lucien Hardy
  Perimeter Institute for Theoretical Physics
- Rafael Sorkin
  Perimeter Institute for Theoretical Physics
- Wayne Myrvold
  Western University
- Howard Barnum
  University of New Mexico
- Joe Henson
  BNP Paribas Asset Management London
- Markus Müller
  Institute for Quantum Optics and Quantum Information (IQOQI) - Vienna
May 30, 2013

PIRSA:13050081
Quantum Information

Quantum Fields and Strings
Towards a realist's interpretation of the path integral

Petros Wallden
University of Athens

May 31, 2013

PIRSA:13050071
Time, cosmology and quantum foundations

Lee Smolin
Perimeter Institute for Theoretical Physics
May 31, 2013

PIRSA:13050072
Quantum Foundations

Cosmology
Characterizing quantum non-locality: a histories approach

Joe Henson
BNP Paribas Asset Management London
May 31, 2013

PIRSA:13050073
Quantum Foundations

Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory
May 30, 2013

PIRSA:13050070
Mathematical physics
The last few years have seen a spate of operational or information-theoretic
derivations (or \reconstructions") of nite-dimensional quantum mechanics [1]. These rest of some strong assumptions. In particular, most assume the state of a composite system is entirely determined by the joint probabilities it assigns to the outcomes of measurements on the component systems. This condition, often called local tomography, is satis ed by neither real nor quaternionic quantum theory. If we are interested in the possibilities for theories more general than orthodox quantum mechanics, we might wish to relax this constraint.
In this talk I will discuss a weaker system of assumptions, involving correla-
tions between a probabilistic system and an isomorphic conjugate system, that leads to a representation of such systems in terms of euclidean Jordan algebras [2]. These have a well-known classi cation as direct sums of real, complex or quaternionic quantum systems, possibly the exceptional Jordan algebra, and spin factors. The last are a form of \bit", characterized by a family of two-valued observables, parametrized by antipodal vectors in a sphere of arbitrary dimension. Orthodox quantum mechanics can be singled out by imposing local tomography, plus the existence of a qubit as additional axioms [3]. However, there is a natural way to form non-signaling, but generally non-locally tomo-graphic, composites of systems based on special euclidean Jordan algebras (that is, excluding the exceptional one). This yields a probabilistic theory strictly, but not wildly, more general than orthodox nite-dimensional QM; one that elegantly uni es real, complex and quaternionic quantum theory, has a simple operational basis, and allows for a spectrum of bits more general than permitted in orthodox quantum theory. Parts of this talk reflect ongoing joint work with Howard Barnum, Matthew Graydon and Cozmin Ududec.
References:
[1] G. Chiribella, M. D'Ariano and P. Perinotti, Phys. Rev. A 84, (2011), 012311-
012350; B. Dakic and C. Brukner, in H. Halvorson (ed.), Deep Beauty, Cambridge,
2011; P. Goyal, Phys. Rev. A 78 (2008), 052120-052146; L. Hardy, arXiv:quant-
ph/0101012 (2001); L. Masanes and M. Mueller, New J. Phys. 13 (2011) ; J. Rau,
Annals of Physics 324 (2009) 2622{2637;
[2] A. Wilce, Conjugates, correlation and quantum mechanics, arXiv:1206.2897 (2012)
[3] H. Barnum and A. Wilce, Local tomography and the Jordan structure of quantum
theory, arXiv:1202.4513, (2012)
Generalizations of Quantum Theory
- Lucien Hardy
  Perimeter Institute for Theoretical Physics
- Rafael Sorkin
  Perimeter Institute for Theoretical Physics
- Wayne Myrvold
  Western University
- Howard Barnum
  University of New Mexico
- Joe Henson
  BNP Paribas Asset Management London
- Markus Müller
  Institute for Quantum Optics and Quantum Information (IQOQI) - Vienna
May 30, 2013

PIRSA:13050081
Quantum Information

Quantum Fields and Strings
Towards a realist's interpretation of the path integral

Petros Wallden
University of Athens

May 31, 2013

PIRSA:13050071

Having a fundamental spacetime view of physics, appears more justified in attempting to construct a quantum theory of gravity. In this talk, motivated by the latter, a path integral approach is adopted and an attempt to construct a self-consistent realistic histories formulation of quantum theory is presented. After revising the histories viewpoint of classical physics, the quantum case is considered. However, the nature of the probabilities arising from the path integral, leads us to alter the classical picture. The new ontology is that of a coevent (or a coarse grained history), and we analyse the consequences of this (relatively) novel proposal.
Time, cosmology and quantum foundations

Lee Smolin
Perimeter Institute for Theoretical Physics
May 31, 2013

PIRSA:13050072
Quantum Foundations

Cosmology
I argue that quantum mechanics cannot usefully be extended to a theory of the whole universe, so the task of quantum foundations is to discover that cosmological theory which reduces to quantum mechanics when restricted to small subsystems of the universe. I argue that that cosmological theory will be based on a global notion of physical time which implies the distinction between past, present and future is real and objective. These motivate two examples of novel formulations of quantum theory: the real ensemble formulation and the principle of precedence. Each may imply departures from the expected quantum evolution for sufficiently large and complex quantum systems.
Characterizing quantum non-locality: a histories approach

Joe Henson
BNP Paribas Asset Management London
May 31, 2013

PIRSA:13050073
Quantum Foundations
Characterising quantum non-locality using simple physical principles has become a hot topic in quantum foundations of late. In the simpler case of local hidden variable models, the space of allowed correlations can be characterised by requiring that there exists a joint probability distribution over all possible experimental outcomes, from which the experimental probabilities arise as marginals. This follows from Bell’s causality condition. But the existing characterisations of quantum correlations are far from being so straightforward.
Motivated by a histories outlook, we propose the following condition: there exists a positive semi-definite matrix in which the indices run over all possible experimental outcomes, from which the experimental probabilities arise as “marginals” in a similar way. This is a much simpler condition than the usual statement of the existence of a quantum model for the probabilities, and suggests an underlying connection with Bell’s derivation of his bound on local correlations. I will outline existing proofs that this condition places strong bounds on correlations consistent with QM, and ask whether it could completely characterise quantum non-locality

Title	Speaker(s)	Date	Talk Type	Info
Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory		2013-05-30	Conference	View details
Generalizations of Quantum Theory	Lucien Hardy, Rafael Sorkin, Wayne Myrvold, Howard Barnum, Joe Henson, Markus Müller	2013-05-30	Conference	View details
Towards a realist's interpretation of the path integral	Petros Wallden	2013-05-31	Conference	View details
Time, cosmology and quantum foundations	Lee Smolin	2013-05-31	Conference	View details
Characterizing quantum non-locality: a histories approach	Joe Henson	2013-05-31	Conference	View details

The Quantum Landscape 2013

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