# Program

## 30 January

Time | Topic |
---|---|

08:30 - 09:00 | Registration (Room E206) |

09:00 - 09:15 | Opening words: Michael Cuffaro, Samuel Fletcher, Johannes Kofler |

09:10 - 09:15 | Welcome: Stephan Hartmann |

09:15 - 10:45 | Keynote:Chris Timpson: Quantum information: Ontological and conceptual aspectsChair: Michael Cuffaro Watch the lecture @ LMUcast |

10:45 - 11:00 | Coffee Break |

11:00 - 11:45 | Gemma De Las Cuevas: Fundamental limitations of purification problemsChair: Michael Cuffaro |

11:45 - 13:30 | Lunch Break |

13:30 - 14:15 | Alexei Grinbaum: If the observer is defined informationally, what is quantum theory?Chair: Patricia Palacios |

14:15 - 15:00 | Vasil Penchev: Quantum information as the information of infinite seriesChair: Patricia Palacios |

15:00 - 15:30 | Coffee Break |

15:30 - 16:15 | Adrien Feix and Časlav Brukner: Superposition of causal ordering between parties as a communication complexity resourceChair: Lucas Clemente |

16:15 - 17:00 | Lucas Dunlap: Would the Existence of CTCs Allow for Nonlocal Signaling?Chair: Lucas Clemente |

17:00 - 17:15 | Break |

17:15 - 18:45 | Keynote:Rüdiger Schack: QBism and the Born ruleChair: Johannes Kofler Watch the Lecture @ LMUcast |

19:15 | Conference dinner: "Georgenhof" |

## 31 January

Time | Topic |
---|---|

09:00 - 10:30 | Keynote:Hans Briegel: Towards quantum artificial intelligenceChair: Johannes Kofler |

10:30 - 11:00 | Coffee Break |

11:00 - 11:45 | Hector Freytes and Giuseppe Sergioli: Non-Separability in the Representation of Fuzzy Structures in Quantum ComputationChair: Carina Prunkl |

11:45 - 12:30 | Sam Fletcher: The Physical Basis of Computation and Computational ComplexityChair: Carina Prunkl |

12:30 - 14:00 | Lunch Break |

14:00 - 14:45 | Ronnie Hermens: The relevance of Gleason’s Theorem for Bayesian interpretations of quantum probabilitiesChair: Wolfgang Pietsch |

14:45 - 15:30 | Gerd Niestegge: Non-classical conditional probability, quantum measurement, and the no-cloning theoremChair: Wolfgang Pietsch |

15:30 - 16:00 | Coffee Break |

16:00 - 16:45 | Kohtaro Tadaki: A Refinement of Quantum Mechanics by Algorithmic RandomnessChair: Sam Fletcher |

16:45 - 17:00 | Break |

17:00 - 18:30 | Keynote:Leah Henderson: Quantum information theory and the quantum stateChair: Sam Fletcher |

18:45 | Informal drinks |

## Abstracts

### Keynote Talks

#### Hans Briegel: Towards quantum artificial intelligence

Studying the ways in which quantum mechanics could be exploited for computation and information processing has lead us to reflect on the very notion of a computational process. In this talk I will first review some ideas and concepts in measurement-based quantum computation and then put them into the context of machine learning and agency. In particular, I will discuss the roles of quantum measurement and indeterminacy as resources for quantum computation, learning, and agency.top

#### Leah Henderson: Quantum information theory and the quantum state

Quantum information theory has given rise to an impressive new array of technological developments, as well as a richer understanding of quantum phenomena. It also potentially has important philosophical implications for understanding the quantum state. Various ideas from quantum information theory point towards the presence of a close analogy between quantum states and probability distributions. In this talk I will explore some of the possibilities this raises for an epistemic interpretation of the quantum state which avoids instrumentalism.top

#### Rüdiger Schack: QBism and the Born rule

By adopting a strictly personalist approach to probability, QBism takes the view that quantum states, and therefore also quantum information, reflect an agent’s personal degrees of belief about the consequences of his actions on the world. The quantum formalism enables the agent to make better decisions in the light of his previous experiences. This talk focuses on the central role played in quantum mechanics by the Born rule, which in QBism has a normative character similar to the rules of probability theory.top

#### Chris Timpson: Quantum Information: Ontological and Conceptual Aspects

In this talk I will explore some ways of thinking about what quantum information is. This topic has a certain intrinsic interest, but it is also important when trying to assess in a careful way what role the concept of information might have to play in fundamental physics. I shall argue for a view which is fairly ontologically deflationary about quantum information (this has significant impact on how we should understand the slogan ‘information is physical’ and for informational immaterialist views) and which sees quantum and classical (Shannon) information both as species of a single genus.top

### Contributed Talks

#### Alexei Grinbaum: If the observer is defined informationally, what is quantum theory?

Quantum mechanics has an orthodox interpretation that relies on the cut between the observer and the quantum system, but it does not define the observer physically. We propose an informational definition based on limited complexity of the strings the observer can store and handle. Using Kolmogorov complexity, we then derive a plausible candidate for quantum theory. We extensively discuss Bohr’s view of classical language and Zurek’s, of information.top

#### Vasil Penchev: Quantum information as the information of infinite series

The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit, can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question.top

#### Ronnie Hermens: The relevance of Gleason’s Theorem for Bayesian interpretations of quantum probabilities

In several publications, Bub and Pitowsky have argued for a Bayesian reading of quantum probabilities as part of their information-theoretical approach to quantum mechanics. Like in the classical case, a key question then is why the credences of an agent should obey the same rules as a (quantum) probability function. The argumentation of Bub and Pitowsky relies strongly on Gleason’s Theorem, which, in this context, in turn relies on associating events with projections. Although this association is seldom questioned, I will explain why it is troublesome in the approach of Bub and Pitowsky.top

#### Adrien Feix and Časlav Brukner: Superposition of causal ordering between parties as a communication complexity resource

In communication complexity scenarios, two or more parties aim to compute a function of their input bit strings, using a limited amount of communication. It is known that quantum states and shared entanglement are useful resources in this context. We present an experimentally implementable multipartite communication complexity scenario which exploits the superposition of ordering between parties as a resource to lower the amount of communication between the parties, compared to the ordinary ordered quantum case.top

#### Lucas Dunlap: Would the Existence of CTCs Allow for Nonlocal Signaling?

I argue that a quantum circuit aided by a closed timelike curve can effect instantaneous nonlocal signaling between spatially distant parties. This implication has been resisted in the quantum information literature. The reason for this, I argue, is that QCIT conceives of quantum theory to be fundamentally formulable in terms of globally inviolable principles, of which No-Signaling is one. Other foundational approaches to quantum theory focus fundamentally on questions of ontology. When allowing CTCs, these approaches make different predictions. This example helps draw out the differences, and outline the kinds of conclusions that can be drawn from each approach.top

#### Gerd Niestegge: Non-classical conditional probability, quantum measurement, and the no-cloning theorem

The no-cloning theorem, an pioneering result of QCIT with profound consequences, is studied in the setting of a quantum logic E with a conditional probability calculus. This is an extension of the classical probability calculus and a mathematical generalization of the Lüders - von Neumann quantum measurement process. A very special type of conditional probability emerges here; it describes the probability for the transition from a past event e to a future event f, is independent of the underlying state, results from the algebraic structure of E only and is invariant under the algebraic morphisms of the quantum logic. This is used to prove a generalized no-cloning theorem in a very basic fashion.top

#### Hector Freytes and Giuseppe Sergioli: Non-Separability in the Representation of Fuzzy Structures in Quantum Computation

In order to establish a connection between quantum computation with mixed states and fuzzy logic of continuous t-norms, we provide a representation of the Lukasiewicz t-norm in terms of quantum operations. To achieve a better efficiency of this representation - without coming into an undesirable increasing of the dimension of the Hilbert space - the strategy we propose is based on the use of non-separable quantum states. The set of Werner states is introduced as an example. These results induce algebraic structures that describe combinational logics for quantum circuits and suggest new form of quantum logics.top

#### Kohtaro Tadaki: A Refinement of Quantum Mechanics by Algorithmic Randomness

The notion of probability plays a crucial role in quantum mechanics. It appears as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure theory, and therefore any operational characterization of the notion of probability is still missing in quantum mechanics. We present an alternative rule to the Born rule based on algorithmic randomness without using the notion of probability. Algorithmic randomness enables us to consider the randomness of an individual infinite sequence. We use a notion in it for specifying the property of results of quantum measurements in an operational way.top

#### Gemma De Las Cuevas, Toby Cubitt, David Perez-Garcia and Michael M. Wolf: Fundamental limitations of purification problems

We show that there exist families of translational invariant (TI) mixed states which have a translational invariant Matrix Product Operator representation valid for all system sizes, but for which there does not exist a TI local purification valid for all sizes. The result holds for periodic boundary conditions and also for classical states. The proof is based on the undecidability of some matrix problems as well as results on matrix product states. This result sheds light on the fundamental limitations that the mathematical formalism of quantum theory imposes on it.top

#### Sam Fletcher: The Physical Basis of Computation and Computational Complexity

Nielsen (1997) and Josza (2004) have raised the possibilities that the theories of computability and computational complexity, respectively, constrain physical law. I shall argue, however, that these proposals are complicated by the fact that both the notions of physical computability and computational complexity presuppose a characterization of the possibilities afforded by physical theory. Insofar as the theories of computability and computational complexity constrain physical theories, they only do so by virtue of their grounding in currently accepted physical theories. Thus these aspects of computer science, despite the novel perspectives they offer, do not independently check physics.