This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
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.
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.
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.
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.
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.
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.
From arXiv: 1806.04937, with Carlo Sparaciari, Carlo Maria Scandolo, Philippe Faist and Jonathan Oppenheim
Recent advances in scaling photonics for universal quantum computation spotlight the need for a thorough understanding of practicalities such as distinguishability in multimode quantum interference. Rather than the usual second quantized approach, we can bring quantum information concepts to bear in first quantization. Distinguishability can then be modelled as entanglement between photonic degrees of freedom, where loss of interference is caused by decoherence due to correlations with an environment carried by the particles themselves. This shows that multiparticle, multimode Fock state
What does it mean for quantum state to be genuinely fully multipartite? Some would say, whenever the state cannot be decomposed as a mixture of states each of which has no entanglement across some partition. I'll argue that this partition-centric thinking is ill-suited for the task of assessing the connectivity of the network required to realize the state.