# Quantum Foundations

This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.

## Seminar Series Events/Videos

May 28 2019 - 3:30pm
Room #: 394
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## A Gleason-type theorem for qubits based on mixtures of projective measurements

Tuesday May 14, 2019

We derive Born’s rule and the density-operator formalism for quantum systems with Hilbert spaces of finite dimension. Our extension of Gleason’s theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

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## Delocalized quantum clocks and relativistic time dilation

Thursday Apr 25, 2019
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The theory of relativity associates a proper time with each moving object via its spacetime trajectory. In quantum theory on the other hand, such trajectories are forbidden. I will discuss an operation approach to exploring this conflict, considering the average time measured by a quantum clock in the weak-field, low-velocity limit. Considering the role of the clock’s state of motion, one finds that all good'' quantum clocks experience the time dilation prescribed by general relativity for the most classical states of motion.

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## Probability in many-world theories

Tuesday Apr 16, 2019
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A common criticism directed against many-world theories is that, being deterministic, they cannot make sense of probability. I argue that, on the contrary, deterministic theories with branching provide us the only known coherent definition of objective probability. I illustrate this argument with a toy many-worlds theory known as Kent's universe, and discuss its limitations when applied to the usual Many-Worlds interpretation of quantum mechanics.

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## Epistemic interpretations of quantum mechanics have a measurement problem

Tuesday Apr 09, 2019
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Epistemic interpretations of quantum theory maintain that quantum states only represent incomplete information about the physical states of the world. A major motivation for this view is the promise to provide a reasonable account of state update under measurement by asserting that it is simply a natural feature of updating incomplete statistical information. Here we demonstrate that all known epistemic ontological models of quantum theory in dimension d ≥ 3, including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly.

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## Quantum Statistical Comparison, Quantum Majorization, and Their Applications to Generalized Resource Theories

Tuesday Feb 26, 2019
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The theory of statistical comparison was formulated (chiefly by David Blackwell in the 1950s) in order to extend the theory of majorization to objects beyond probability distributions, like multivariate statistical models and stochastic transitions, and has played an important role in mathematical statistics ever since. The central concept in statistical comparison is the so-called "information ordering," according to which information need not always be a totally ordered quantity, but often takes on a multi-faceted form whose content may vary depending on its use.

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## Numerical decomposition of finite dimensional group representations

Wednesday Feb 13, 2019
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Group representations are ubiquitous in quantum information theory. Many important states or channels are invariant under particular symmetries: for example depolarizing channels, Werner states, isotropic states, GHZ states. Accordingly, computations involving those objects can be simplified by invoking the symmetries of the problem. For that purpose, we need to know which irreducible representations appear in the problem, and how.

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## Quantum Mechanics without Wave Functions: a Signed Particle Formulation

Tuesday Feb 05, 2019
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Recently, a new formulation of quantum mechanics was suggested which is based on the evolution of classical particles, provided with a sign, rather than standard wave functions. This allows several advantages over other approaches: from a theoretical perspective, it offers a more intuitive framework while, from a numerical point of view, it allows the simulation of complex systems with relatively small computational resources. In this talk, I will first go through the tenets of this new approach.

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## Quantum Tasks in Relativistic Spacetime

Monday Feb 04, 2019
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In this talk I will set out two new contributions to the study of operational tasks in a relativistic quantum setting. First, I will present a generalisation of the task known as ‘summoning,’ in which an unknown quantum state is supplied to an agent and must be returned at a specified point when a corresponding call is made. I will show that when this task is generalised to allow for more than one call to be made, an apparent paradox arises: the extra freedom makes it strictly harder to complete the task.

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## The first law of general quantum resource theories

Tuesday Jan 29, 2019
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From arXiv: 1806.04937, with Carlo Sparaciari, Carlo Maria Scandolo, Philippe Faist and Jonathan Oppenheim

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## Quantum non-locality from a sequence of experiments perspective

Tuesday Jan 22, 2019
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