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Here, you can find an overview of some of the research problems I have studied, together with a selection of representative works.
Entropy
Entropy measures uncertainty and plays a central role in information theory and quantum physics. Part of my research concerns how entropy behaves when a probability distribution or a quantum state is slightly perturbed, a question that becomes particularly subtle for infinite-dimensional systems. I study continuity bounds, which quantify how much an entropy can vary when the underlying state changes by a given amount. Such bounds are also useful in quantum information theory for deriving bounds on the capacities of quantum channels. My work includes the derivation of new entropic inequalities and tight continuity bounds, as well as optimal bounds for infinite-dimensional quantum systems subject to physically meaningful energy constraints.
Selected papers
(Koenraad Audenaert, Bjarne Bergh, Nilanjana Datta, Michael G. Jabbour, Ángela Capel and Paul Gondolf)
We established a new fundamental inequality for the von Neumann entropy that gives a tight bound on the entropy difference between two quantum states. It provides a refinement of the well-known Audenaert-Fannes inequality and remains valid in infinite dimensions. We used it to derive new continuity bounds for quantities including the quantum conditional entropy and the quantum relative entropy.
(Simon Becker, Nilanjana Datta, Michael G. Jabbour and Maxim E. Shirokov)
In infinite-dimensional quantum systems, meaningful continuity bounds generally require an energy constraint. We derived a globally optimal continuity bound for the von Neumann entropy under general energy constraints, valid for arbitrary Hamiltonians satisfying the Gibbs hypothesis. This completely solves the problem of finding the optimal bound in this setting, extending previous results that applied only when the two states were sufficiently close.
Majorization
Majorization is a mathematical way of comparing how ordered or disordered two probability distributions or quantum states are. It provides a stronger notion of comparison than entropy alone, since a majorization relation implies inequalities for a whole family of measures of uncertainty. I have used majorization to study the action of bosonic quantum channels and to establish ordering relations between their output states. Majorization has also played an important role in my work on continuity bounds for entropies, where it provides a powerful tool for identifying extremal states and deriving optimal inequalities. More broadly, I am interested in extending the theory of majorization to continuous quantum systems and in understanding its mathematical structure and connections with entropy.
Selected papers
(Zacharie Van Herstraeten, Michael G. Jabbour and Nicolas J. Cerf)
Quantum states can be represented in phase space by Wigner functions, which share many properties with ordinary probability distributions when they are positive. We showed that continuous majorization provides a natural framework for comparing the uncertainty of such quantum states. In particular, we conjectured that every positive Wigner function is more disordered than that of a pure Gaussian state, such as the vacuum state, and proved this conjecture for an important class of non-Gaussian states. This majorization relation implies, at once, a whole family of entropic inequalities in quantum phase space.
(Alexander Stévins, Michael G. Jabbour, Serge Deside and Nicolas J. Cerf)
Majorization not only defines an ordering between probability distributions; it also endows them with the mathematical structure of a lattice. We uncovered two fundamental majorization relations within this lattice that imply general inequalities for a broad class of functions. As a consequence, we established supermodularity and subadditivity properties for several important measures of entropy, including the Shannon, Rényi and Tsallis entropies. These results show that some entropic inequalities originate from more fundamental relations at the level of majorization itself.
Quantum interference
Quantum interference between identical particles is one of the characteristic manifestations of quantum physics. I am interested in uncovering the mathematical structures underlying these phenomena, particularly for bosonic systems such as photons. My work has explored interference in beam splitters and quantum amplifiers, as well as fundamental connections between the contrasting behaviours of bosons and fermions. These investigations have also led to new mathematical identities involving the permanent and determinant of matrices, two quantities that naturally describe multiparticle interference for bosons and fermions, respectively.
Selected papers
(Nicolas J. Cerf and Michael G. Jabbour)
The Hong-Ou-Mandel effect describes how two identical bosons interfere when they meet at a balanced beam splitter. We showed that a mathematical duality between a beam splitter and a quantum amplifier leads to a new interference effect in which the relevant indistinguishability occurs in time rather than in space. We identified this phenomenon as a general consequence of bosonic quantum dynamics described by Bogoliubov transformations. The predicted effect was subsequently observed experimentally.
(Michael G. Jabbour and Nicolas J. Cerf)
Bosons and fermions exhibit apparently opposite interference behaviours, most famously bosonic bunching and fermionic antibunching. We established a fundamental relation that brings the transition probabilities of bosons and fermions together in a single equation, revealing a complementarity that is independent of the details of the interferometer. For two particles, this implies that the average of the bosonic and fermionic probabilities coincides with the probability for distinguishable classical particles. The same relation yields a new mathematical identity connecting the permanent and determinant of an arbitrary complex matrix, extending a result that dates back to the nineteenth century.
Bell nonlocality
Bell nonlocality describes correlations between distant quantum systems that cannot be reproduced by any classical model based on local hidden variables. Although entanglement is necessary for such correlations, entanglement and Bell nonlocality are distinct notions. I am interested in mathematically characterising this distinction in bosonic systems, and in determining when the correlations produced by Gaussian quantum states and experimentally relevant measurements can still admit a local classical description.
Selected papers
(Michael G. Jabbour and Jonatan Bohr Brask)
We developed a general method for constructing local hidden-variable models for measurements performed on bosonic Gaussian states. The method works by transferring part of the intrinsic Gaussian noise of the state to the measurements, leading to a simple sufficient criterion for locality. We applied it to displaced photodetection on a two-mode squeezed state and identified a range in which the state remains entangled while its measurement statistics nevertheless admit a local hidden-variable model. This provides a concrete illustration of the distinction between quantum entanglement and Bell nonlocality.
Quantum thermodynamics
Quantum thermodynamics investigates how concepts such as energy, work, entropy and irreversibility behave at the quantum level. My work in this area has focused particularly on bosonic systems. I have studied the extraction of work from multipartite quantum systems, the possibility of generating entanglement using thermal environments at different temperatures, and the ordering properties of bosonic channels interacting with passive environments. Majorization provides a useful connection between some of these questions and the notion of thermodynamic disorder. More recently, I have been interested in coarse-grained descriptions of quantum systems and in how different notions of entropy can be connected to the second law of thermodynamics.
Selected papers
(Joseph Schindler, Philipp Strasberg, Niklas Galke, Andreas Winter and Michael G. Jabbour)
Coarse-graining describes a system when only limited information about its microscopic state is available, and different approaches have led to different notions of entropy. We introduced a general definition that unifies observational entropy with the maximum-entropy principle of statistical mechanics by interpreting physical constraints as information-theoretic priors. The resulting framework encompasses many commonly used entropies, leads to new entropy-increase theorems and connections with the second law, and avoids some difficulties that arise for traditional observational entropy in infinite-dimensional systems.
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