Entropy, majorization and thermodynamics in general probabilistic theories

In this note we lay some groundwork for the resource theory of thermodynamics in general probabilistic theories (GPTs). We consider theories satisfying a purely convex abstraction of the spectral decomposition of density matrices: that every state has a decomposition, with unique probabilities, into perfectly distinguishable pure states. The spectral entropy, and analogues using other Schur-concave functions, can be defined as the entropy of these probabilities. We describe additional conditions under which the outcome probabilities of a fine-grained measurement are majorized by those for a spectral measurement, and therefore the "spectral entropy" is the measurement entropy (and therefore concave). These conditions are (1) projectivity, which abstracts aspects of the Lueders-von Neumann projection postulate in quantum theory, in particular that every face of the state space is the positive part of the image of a certain kind of projection operator called a filter; and (2) symmetry of transition probabilities. The conjunction of these, as shown earlier by Araki, is equivalent to a strong geometric property of the unnormalized state cone known as perfection: that there is an inner product according to which every face of the cone, including the cone itself, is self-dual. Using some assumptions about the thermodynamic cost of certain processes that are partially motivated by our postulates, especially projectivity, we extend von Neumann's argument that the thermodynamic entropy of a quantum system is its spectral entropy to generalized probabilistic systems satisfying spectrality.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Computational irreducibility and compatibilism: towards a formalization

If our actions are determined by the laws of nature, can we meaningfully claim to possess free will? Compatibilists argue that the answer is yes, and that free will is compatible with complete determinism. Previously, it has been suggested that the notion of computational irreducibility can shed light on this relation: it implies that there cannot in general be "shortcuts" to the decisions of agents, explaining why deterministic agents often appear to have free will. In this paper, we introduce a variant of computational irreducibility that intends to capture more accurately aspects of actual (as opposed to apparent) free will: computational sourcehood, i.e. the phenomenon that the successful prediction of a process' outputs must typically involve an almost-exact representation of the relevant features of that process, regardless of the time it takes to arrive at the prediction. We conjecture that many processes have this property, and we study different possibilities for how to formalize this conjecture in terms of universal Turing machines. While we are not able to settle the conjecture, we give several results and constructions that shed light on the quest for its correct formulation.Comment: 15 pages, 1 figur

Internal quantum reference frames for finite Abelian groups

Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained treatment of such quantum reference frames (QRFs) for the case when the underlying configuration space is a finite Abelian group, significantly extending our previous work (Quantum 5, 530 (2021)). The simplicity of this setup admits a fully rigorous quantum information-theoretic analysis, while maintaining sufficient structure for exploring many of the conceptual and structural questions also pertinent to more complicated setups. We exploit this to derive several important structures of constraint quantization with quantum information-theoretic methods and to reveal the relation between different approaches to QRF covariance. In particular, we characterize the "physical Hilbert space" -- the arena of the "perspective-neutral" approach -- as the maximal subspace that admits frame-independent descriptions of purifications of states. We then demonstrate the kinematical equivalence and, surprising, dynamical inequivalence of the "perspective-neutral" and the "alignability" approach to QRFs. While the former admits unitaries generating transitions between arbitrary subsystem relations, the latter, remarkably, admits no such dynamics when requiring symmetry-preservation. We illustrate these findings by example of interacting discrete particles, including how dynamics can be described "relative to one of the subsystems".Comment: 22 pages, 1 figure. V2: close to published versio

Towards interpretable quantum machine learning via single-photon quantum walks

Variational quantum algorithms represent a promising approach to quantum machine learning where classical neural networks are replaced by parametrized quantum circuits. However, both approaches suffer from a clear limitation, that is a lack of interpretability. Here, we present a variational method to quantize projective simulation (PS), a reinforcement learning model aimed at interpretable artificial intelligence. Decision making in PS is modeled as a random walk on a graph describing the agent's memory. To implement the quantized model, we consider quantum walks of single photons in a lattice of tunable Mach-Zehnder interferometers trained via variational algorithms. Using an example from transfer learning, we show that the quantized PS model can exploit quantum interference to acquire capabilities beyond those of its classical counterpart. Finally, we discuss the role of quantum interference for training and tracing the decision making process, paving the way for realizations of interpretable quantum learning agents.Comment: 11+8 pages, 6+9 figures, 2 tables. F. Flamini and M. Krumm contributed equally to this wor

FOUGERE: User-Centric Location Privacy in Mobile Crowdsourcing Apps

International audienceMobile crowdsourcing is being increasingly used by industrial and research communities to build realistic datasets. By leveraging the capabilities of mobile devices, mobile crowdsourcing apps can be used to track participants' activity and to collect insightful reports from the environment (e.g., air quality, network quality). However, most of existing crowdsourced datasets systematically tag data samples with time and location stamps, which may inevitably lead to user privacy leaks by discarding sensitive information. This paper addresses this critical limitation of the state of the art by proposing a software library that improves user privacy without compromising the overall quality of the crowdsourced datasets. We propose a decentralized approach, named Fougere, to convey data samples from user devices to third-party servers. By introducing an a priori data anonymization process, we show that Fougere defeats state-of-the-art location-based privacy attacks with little impact on the quality of crowd-sourced datasets