Berry Groisman’s research while affiliated with University of Cambridge and other places

An attempt to resolve the controversy regarding the solution of the Sleeping Beauty Problem in the framework of the Many-Worlds Interpretation led to a new controversy regarding the Quantum Sleeping Beauty Problem. We apply the concept of a measure of existence of a world and reach the solution known as ‘thirder’ solution which differs from Peter Lewis’s ‘halfer’ assertion. We argue that this method provides a simple and powerful tool for analysing rational decision theory problems.

The Sleeping Beauty Problem is analysed within the framework of the Many-Worlds Interpretation of Quantum Theory. The view of the Many-Worlds Interpretation as fundamentally deterministic theory with no place for objective uncertainty is advocated. The main concepts of this version of the Many-Worlds Interpretation are reviewed and it is shown how their application leads to a Thirder solution to the Sleeping Beauty Problem, and not to the Halfer solution as it was claimed by Peter Lewis.

We propose a toy-model theory, that mimics various characteristic features of quantum mechanics. Unlike the toy-models previously studied in the literature, our toy-model allows for an observer to have a full knowledge of a system's real (ontic) state. This is achieved by introducing domains of disjointness, that is by allowing ontic states to be "non-orthogonal". The observer can perform tests which allow her to distinguish between the states in a single domain of disjointness, but not between all ontic states at once. The consequence of this assumption is that the ontic picture is extended to include joint states of two or more systems. This effectively amounts to emergence of entanglement in the model. We argue that these features, albeit being a "non-classical" element in the theory, support the view that quantum-mechanical states are ontic states.

Since its discovery quantum teleportation has often been seen as a manifestation, indeed the epitome, of the very paradoxical and mysterious nature of quantum theory itself. It is commonly regarded as genuinely quantum and essentially paradoxical. Although a common approach to teleportation amongst physicists nowadays is a somewhat operational one, some researchers are making an effort to deflate the above views. On the one hand, it was recently argued that the paradox of information transfer taking place in teleportation is dissolved (Timpson, 2006) by appealing the very notion of information. On the other hand, it was demonstrated that some classical versions of teleportation retain its important features, which hitherto were considered genuinely quantum (Cohen, 2003; Collins&Popescu, 2002; Hardy, 1999; Mor, 2006; Spekkens, 2007). I will present a special version of a quantum teleportation protocol which is in a sense split into classical and quantum steps. This description provides us with a unified picture of teleportation in both domains. It will be explicitly shown how classical teleportation is embedded in the quantum protocol. Moreover, the classical step can be successfully accomplished even if the state shared by the parties is completely disentangled [this is consistent with the result obtained in (Wang, 2005)]. Yet, all the (apparent) paradoxical features usually associated with quantum teleportation are clearly present in this step. In particular, this demonstrates that entanglement cannot be ultimately responsible and not necessary for the (paradoxical?) information transfer. Thus, even if one considers teleportation as mysterious, all its mysteries are shifted from quantum domain into purely classical one.

The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle ([1984]), would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach and without eliminating this inconsistency, the approach cannot be regarded as scientific. The Sleeping Beauty Problem is just such an example. The existing attempts to solve the problem fall into three categories. The first two share the view that new evidence is absent, but differ about the conclusion of whether Sleeping Beauty should change her belief or not, and why. The third category is characterized by the view that, after all, new evidence (although hidden from the initial view) is involved. My solution is radically different and does not fall in either of these categories. I deflate the paradox by arguing that the two different degrees of belief presented in the Sleeping Beauty Problem are in fact beliefs in two different propositions, i.e. there is no need to explain the (un)change of belief.

The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle ([1984]), would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach, and without eliminating this inconsistency, the approach cannot be regarded as scientific. The Sleeping Beauty Problem is just such an example. The existing attempts to solve the problem fall into three categories. The first two share the view that new evidence is absent, but differ about the conclusion of whether Sleeping Beauty should change her belief or not, and why. The third category is characterized by the view that, after all, new evidence (although hidden from the initial view) is involved. My solution is radically different and does not fall into either of these categories. I deflate the paradox by arguing that the two different degrees of belief presented in the Sleeping Beauty Problem are in fact beliefs in two different propositions, i.e., there is no need to explain the (un)change of belief. • The Sleeping Beauty Problem • The Problem Deflated • 2.1From contradiction to consistency • 2.2The inanimate version • 2.3Back to SB • Summary

Entangling and disentangling capacities are the key manifestation of the nonlocal content of a quantum operation. A lot of effort has been put recently into investigating (dis)entangling capacities of unitary operations, but very little is known about capacities of non-unitary operations. Here we investigate (dis)entangling capacities of unital CPTP maps acting on two qubits.

Entanglement is one of the pillars of quantum mechanics and quantum information processing, and as a result the quantumness of nonentangled states has typically been overlooked and unrecognized. We give a robust definition for the classicality versus quantumness of a single multipartite quantum state, a set of states, and a protocol using quantum states. We show a variety of nonentangled (separable) states that exhibit interesting quantum properties, and we explore the ``zoo'' of separable states; several interesting subclasses are defined based on their diagonalizing bases, and their non-classical behavior is investigated.

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: the erasure of one bit of information in a computational device is necessarily accompanied by a generation of kTln2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. Norton [2005. Eaters of the lotus: Landauer's principle and the return of Maxwell's demon. Studies in History and Philosophy of Modern Physics, 36, 375–411] and Maroney [2005. The (absence of a) relationship between thermodynamic and logical reversibility. Studies in History and Philosophy of Modern Physics, 36, 355–374] both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers a method that he claims instantiates the operation Reset in a thermodynamically reversible way.In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences (assuming the second law of thermodynamics). We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation ‘Reset’, and thereby recover the quantitative form of Landauer's Principle.

The problem of the reliable transfer of entanglement from one pure bipartite quantum state to another using local operations is analyzed. It is shown that in the case of qubits the amount that can be transferred is restricted to the difference between the entanglement of the two states. In the presence of a catalytic state the range of the transferrable amount broadens to a certain degree.