Quantum Foundations

In this talk, I will explore a timeless interpretation of quantum mechanics of closed systems, solely in terms of path integrals in non-relativistic timeless configuration space. What prompts a fresh look at the foundational problems in this context, is the advent of multiple gravitational models in which Lorentz symmetry is only emergent. In this setting, I propose a new understanding of records as certain relations between two configurations, the recorded one and the record-holding one. These relations are formalized through  a factorization of the amplitude kernel, which forbids unwanted 'recoherence' of branches. On this basis, I show that in simple cases the Born rule is consistent with counting the relative density of observers with the same records. Furthermore, unlike what occurs in consistent histories,  in this context there is indeed a preferred notion of coarse-grainings: those centered around piece-wise classical paths in configuration space (with a certain radius).  Thus, this new understanding  claims to resolve aspects of the measurement problem which are still deemed controversial in the standard approaches (but which probably leaves others open...).

In this talk we will discuss the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that any set of measurements that is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR steering, a form of quantum nonlocality. This implies that EPR steering and (non) joint measurability can be viewed as equivalent. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. This suggest the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model. Finally, we discuss applications of these results to problems in joint mesurability, and for EPR steering using randomly chosen measurements.

To best distinguish between classical and non-classical models of nature requires a good notion of classicality. I will argue that noncontextuality is a good candidate for this notion. Until now, certain theoretical and experimental roadblocks have stood in the way of a test of noncontextuality which is free of unattainable experimental idealizations. I will present solutions to these roadblocks as well as the results of an experimental test.

One necessity to avoid the measurement problem in quantum mechanics is a clear ontology. Such an ontology is for instance provided by Bohmian mechanics. In the non-relativistic regime, Bohmian mechanics is a theory about particles whose motion is governed by a velocity field. The latter is generated by a wave

function solving the Schrödinger equation. In view of Feynman's criticism towards classical field theory one may wonder whether such a complex object as the wave function is needed to account for quantum phenomena. After all the value of the velocity field, i.e., of the wave function, is only needed in the vicinity of the configuration of the particle positions, however, it is defined everywhere in configuration space, even in places where the configuration might never roam.  In a joint work with M. Hall and H. Wiseman we were able to formulate an approach to quantum mechanics that is capable to describe typical quantum phenomena like interference without a wave function, having only particles.  This approach comes at the cost of introducing many classical worlds, hence the name Many-Interacting-Worlds approach (MIW). In MIW the force on each particle is given by 1) Newton's force describing the interaction within each world and 2) an additional force term describing an interaction between the worlds.  Similar approaches have been suggested by B. Poirier and C. Sebens. I will give an overview on MIW, discuss the nature of its equations of motion, and its empirical import.

Using quantum control in foundational experiments allows new theoretical and experimental possibilities. We show how, e.g.,  quantum controlling devices reverse a temporal ordering in  detection. We consider probing of wave–particle duality in   quantum-controlled and the entanglement-assisted delayed-choice experiments. Then we discuss other situations where quantum control may be useful, and finally demonstrate how the techniques we developed are applied to the study of  consistency of the classically reasonable requirements.  In a version of the delayed-choice experiment which ostensibly combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity we show that these ideas are incompatible with any theory, not only with quantum mechanics.

 It is well known - to those who know it - that noise and randomness can enhance signal resolution. I'll present an easy-to-follow example from digital audio that illustrates the way in which adding noise ("dither") prior to measurement enhances the accuracy with which we are able to distinguish the features of the sound or image. I will then explore the way in which the environmental interactions prior to measurement ordinarily characterized as environment-induced decoherence may play a similar role.  The paradoxical conclusion is that the quasiclassical behavior associated with such systems may be a more accurate representation of the quantum world than what we think of as fully "quantum" behavior, which may in turn be artifactual, the result of errors similar to those introduced by the discretization (also known as "quantization") of data in digital audio and imaging.

We present a formal logic modeling some aspects of the behavior of the quantum measurement process, and study some properties of the models of this logic, from which we deduce some characteristics that any such model should verify. In the case of a Hilbert space of dimension at least 3, we then show that no model can lead to the prediction with certainty of more than one atomic outcome. Moreover, if the Hilbert space is finite dimensional, we can precisely describe the structure of the predictions of any model of our logic. As a consequence, we also prove that all the models of our logic make exactly the same predictions regarding whether a given sequence of outcomes is possible.

This talk touches on three questions regarding the ontological status of quantum states using the ontological models

framework: it is assumed that a physical system has some underlying ontic state and that quantum states correspond to probability distributions over these ontic states.

The first question is whether or not quantum states are necessarily real---that is, whether or not the distributions for different quantum states must be disjoint. The PBR theorem proves the reality of quantum states by making assumptions about the ontic structure of bipartite systems, assumptions that have been challenged. Recent work has therefore concentrated on single systems, producing theorems proving the existence of pairs of quantum states whose overlap region on the ontic state space is very small.

The second question is whether the ontology of a quantum system can be macro-realist---that is, can there be "macroscopic" quantities which always have determinate values? The Leggett-Garg inequalities claim to rule out this possibility, but this conclusion has been disputed.

The third question is less familiar: Must quantum superpositions be ontic? That is, for some superposition with respect to some orthonormal basis, must ontic states exist which can be obtained by preparing the superposition, but not by preparing any of the basis states? In other words, can Schrödinger's cat always be either alive xor dead?

The last decade has seen a wave of characterizations of quantum theory using the formalism of generalized probability theory.

In this talk, I will introduce a novel operational approach to characterizing and reconstructing quantum theory which puts an observer’s information acquisition -- rather than the probability structure – centre stage. In particular, we consider an observer interrogating a system with binary questions and explain how an elementary set of rules governing the observer’s acquisition of information about the system leads to qubit quantum theory. The derivation is constructive, elucidating, among other things, the origin of entanglement, monogamy and more generally the correlation structure. This approach also yields a new characterization of pure states in terms of ‘conserved informational charges’ which, in turn, define the unitary group.

After a brief motivation of this question, the presentation is divided in two parts. We first introduce the principle of quantum information causality, which states the maximum amount of quantum information that a transmitted quantum system can communicate as a function of its Hilbert space dimension, independently of any quantum physical resources previously shared by the communicating parties. The second part of the talk considers superdense coding within the framework of general probabilistic theories and addresses the question of why in quantum theory, no more than two bits can be communicated by transmission of a single, entangled, qubit. We introduce hyperdense coding in general probabilistic theories: superdense coding in which N

> 2 bits are communicated by transmission of a system  that locally

encodes at most one bit, and present protocols with N arbitrarily large. Our hyperdense coding protocols imply superadditive classical

capacities: two entangled systems can encode N > 2 bits, even though each system locally encodes at most one bit. Our protocols violate either a reversibility condition or tomographic locality.

The Church-Turing thesis is one of the pillars of computer science; it postulates that every classical system has equivalent computability power to the so-called Turing machine. While this thesis is crucial for our understanding of computing devices, its implications in other scientific fields have hardly been explored. What if we consider the Church-Turing thesis as a law of nature? In this talk I will present our first results in connection with quantum information theory [1] by showing that computer science laws have profound implications for some of the most fundamental results of quantum theory.  First I will show how they question our knowledge on what a mixed quantum state is, as we identified situations in which ensembles of quantum states defining the same mixed state, indistinguishable according to the quantum postulates, do become distinguishable when prepared by a computer (or any classical system). Then I will introduce a new loophole for Bell-like experiments: if some of the parties in a Bell-like experiment use a computer to decide which measurements to make, then the computational resources of an eavesdropper have to be limited in order to have a proper observation of non-locality.

Pure states and pure transformations play a crucial role in most of the recent reconstructions of quantum theory. In the frameworks of general probabilistic theories, purity is defined in terms of probabilistic mixtures and bears an intuitive interpretation of ``maximal knowledge" of the state of the system or of the evolution undergone by it.  On the other hand, many quantum features do not need the probabilistic structure of the theory. For example, Schumacher and Westmoreland formulated a toy theory that only specifies which events are possible (without quantifying they probability) and still reproduces a large number of quantum features. In this talk I will provide a probability-free definition of pure states and pure transformations, which can expressed in the categorical framework of process theories developed by Abramsky and Coecke and coincides with the usual notion under standard assumptions. Building on this definition, I will present a probability-free version of the purification principle, which allows one to retrieve a large number of quantum features even in the lack of probabilistic structure. This work is part of a larger programme that aims at drawing the line between those aspects of quantum theory that can be defined solely in terms of operations in a circuit and those that rely on the subjective expectations of an agent.

Related works:  
-GC, Distinguishability and copiability of programs in general process theories, arXiv:1411.3035;  
-Categorical purification, http://www.cs.ox.ac.uk/CQM2014/programme/Giulio.pdf 
-GC, G. M. D'Ariano, and P. Perinotti, Probabilistic theories with purification, Phys. Rev. A 81, 062348 (2010)