- Calgary, AB, Canada
- From 2009 to 2012, I studied for a Bachelor's degree in Physics at the University of Padua, Italy, where I graduated ... moreFrom 2009 to 2012, I studied for a Bachelor's degree in Physics at the University of Padua, Italy, where I graduated in 2012 with 110/110 summa cum laude (full marks with honours), with a BSc thesis on the foundations of special relativity (A critical analysis of the postulates of special relativity", supervisor: Kurt Lechner).
After that, from 2012 to 2014, I studied for a Master's degree in Theoretical Physics again at the University of Padua, Italy, where I graduated in 2014 with 110/110 summa cum laude (full marks with honours), with an MSc thesis on the foundations of quantum mechanics and general probabilistic theories (Entanglement and thermodynamics in general probabilistic theories, supervisor: Giulio Chiribella, internal supervisor: Pieralberto Marchetti).
From 2009 to 2014, I was part of an excellence programme at the University of Padua, Italy, the Galilean School of Higher Education. Every year, the Galilean School of Higher Education admits 14 fresher students in the whole area of sciences. Admission is subjected to passing a demanding entrance examination. Students are then required to maintain a high GPA for their entire degree course, and to take additional and specially dedicated courses, otherwise they are expelled. Students are granted free meals, free accommodation, plus a yearly textbook allowance. At the end, a dedicated Master’s degree is awarded upon successful completion of all the Galilean degree course.
I graduated in 2015 with 100/100 summa cum laude (full marks with honours), with a thesis on resource theories in general probabilistic theories (A generalized approach to resource theories, supervisor: Pieralberto Marchetti).
From 2015 to 2018 I was a PhD student at the University of Oxford, Department of Computer Science and St. Anne's College, UK, under the supervision of Jon Barrett. Here I worked on topics in quantum foundations and quantum information theory, especially on general probabilistic theories.
I defended my PhD thesis (Information-theoretic foundations of thermodynamics in general probabilistic theories) in October 2018, passing with no corrections.
Before going to Oxford as a PhD student, I did one year (2014 - 2015) of doctoral research at Tsinghua University, IIIS, Beijing, China, under the supervision of Giulio Chiribella.
From November 2018 to September 2020 I was a postdoctoral researcher in Gilad Gour's group, at the University of Calgary, AB, Canada, Department of Mathematics & Statistics.
Since September 2020 I have been assistant professor of mathematical physics at the University of Calgary, AB, Canada, Department of Mathematics & Statistics.(From 2009 to 2012, I studied for a Bachelor's degree in Physics at the University of Padua, Italy, where I graduated in 2012 with 110/110 summa cum laude (full marks with honours), with a BSc thesis on the foundations of special relativity (A critical analysis of the postulates of special relativity", supervisor: Kurt Lechner).<br /><br />After that, from 2012 to 2014, I studied for a Master's degree in Theoretical Physics again at the University of Padua, Italy, where I graduated in 2014 with 110/110 summa cum laude (full marks with honours), with an MSc thesis on the foundations of quantum mechanics and general probabilistic theories (Entanglement and thermodynamics in general probabilistic theories, supervisor: Giulio Chiribella, internal supervisor: Pieralberto Marchetti).<br /><br />From 2009 to 2014, I was part of an excellence programme at the University of Padua, Italy, the Galilean School of Higher Education. Every year, the Galilean School of Higher Education admits 14 fresher students in the whole area of sciences. Admission is subjected to passing a demanding entrance examination. Students are then required to maintain a high GPA for their entire degree course, and to take additional and specially dedicated courses, otherwise they are expelled. Students are granted free meals, free accommodation, plus a yearly textbook allowance. At the end, a dedicated Master’s degree is awarded upon successful completion of all the Galilean degree course.<br />I graduated in 2015 with 100/100 summa cum laude (full marks with honours), with a thesis on resource theories in general probabilistic theories (A generalized approach to resource theories, supervisor: Pieralberto Marchetti).<br /><br />From 2015 to 2018 I was a PhD student at the University of Oxford, Department of Computer Science and St. Anne's College, UK, under the supervision of Jon Barrett. Here I worked on topics in quantum foundations and quantum information theory, especially on general probabilistic theories.<br />I defended my PhD thesis (Information-theoretic foundations of thermodynamics in general probabilistic theories) in October 2018, passing with no corrections.<br /><br />Before going to Oxford as a PhD student, I did one year (2014 - 2015) of doctoral research at Tsinghua University, IIIS, Beijing, China, under the supervision of Giulio Chiribella.<br /><br />From November 2018 to September 2020 I was a postdoctoral researcher in Gilad Gour's group, at the University of Calgary, AB, Canada, Department of Mathematics & Statistics.<br /><br />Since September 2020 I have been assistant professor of mathematical physics at the University of Calgary, AB, Canada, Department of Mathematics & Statistics.)edit
Research Interests:
Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems, their dynamics, and interaction. Since the inception of quantum theory, it has... more
Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems, their dynamics, and interaction. Since the inception of quantum theory, it has been debated whether complex numbers are actually essential, or whether an alternative consistent formulation is possible using real numbers only. Here, we attack this long-standing problem both theoretically and experimentally, using the powerful tools of quantum resource theories. We show that - under reasonable assumptions - quantum states are easier to create and manipulate if they only have real elements. This gives an operational meaning to the resource theory of imaginarity, for which we identify and answer several important questions. This includes the state-conversion problem for all qubit states and all pure states of any dimension, and the approximate imaginarity distillation for all quantum states. As an application, we show that imaginarity plays a crucial role for state discrimination: there exist quantum states which can be perfectly distinguished via local operations and classical communication, but which cannot be distinguished with any nonzero probability if one of the parties has no access to imaginarity. This phenomenon proves that complex numbers are an indispensable part of quantum mechanics, and we also demonstrate it experimentally with linear optics.
Research Interests:
The most general quantum object that can be shared between two distant parties is a bipartite quantum channel. In general, bipartite channels can produce entangled states, and can be used to simulate quantum operations that are not... more
The most general quantum object that can be shared between two distant parties is a bipartite quantum channel. In general, bipartite channels can produce entangled states, and can be used to simulate quantum operations that are not local. When the input dimensions are trivial, a bipartite channel can be viewed as a bipartite state, and when the output systems are classical the channel can be viewed as a bipartite POVM. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, for the first time we rigorously study the entanglement of bipartite channels. We follow a top-down approach, starting from general resource theories of processes, for which we present a new construction of a complete family of monotones, valid in all resource theories where the set of free superchannels is convex. In this setting, we define various general resource-theoretic protocols and resource monotones, which are then applied to the case of entanglement of bipartite channels. We focus in particular on the resource theory of PPT entanglement. Our definition of PPT superchannels is new, as we do not assume that it can be realized by pre- and post-PPT channels. This leads to a greater mathematical simplicity that allows us to express all resource protocols and monotones in terms of semidefinite programs. Along the way, we generalize the negativity measure to bipartite channels, and show that another monotone, the max-logarithmic-negativity, has an operational interpretation as the exact asymptotic entanglement cost of a bipartite channel. Finally, we show that it is not possible to distill entanglement out of bipartite PPT channels under any set of free superchannels that can be used in entanglement theory, leading us in particular to the discovery of bound entangled POVMs.
Research Interests:
Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement.... more
Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly those transforming quantum channels into CPTNI maps even when tensored with the identity supermap. We link this result to the fact that the principle of causality fails in the theory of quantum supermaps.
Research Interests:
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these... more
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.
Research Interests:
In this work, we use the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes. By considering multi-slit experiments, we show that the theory... more
In this work, we use the recently introduced double-dilation construction by Zwart and Coecke to construct a new categorical probabilistic theory of density hypercubes. By considering multi-slit experiments, we show that the theory displays higher-order interference of order up to fourth. We also show that the theory possesses hyperdecoherence maps, which can be used to recover quantum theory in the Karoubi envelope.
Research Interests:
An essential scientific question is whether a description of Nature can be formulated without knowing its ultimate physical theory, but instead by simply relying on some fundamental principles that account for experimental data. Here we... more
An essential scientific question is whether a description of Nature can be formulated without knowing its ultimate physical theory, but instead by simply relying on some fundamental principles that account for experimental data. Here we show that for the emergence of objectivity the answer is positive, and it is based solely on the Causality principle. In this respect, we formulate a necessary requirement for a theory to be fundamental, illustrating its usefulness with a non-trivial example. We provide a natural definition of the decoherence process valid in all fundamental causal theories, and demonstrate its extreme departure from quantum decoherence in its behavior. Remarkably, despite the broad range of theories and process studied, we prove that the so-called Spectrum Broadcast Structure characterizes all objective states in every fundamental causal theory, exactly as in quantum mechanics. Our results, including especially the stark contrast between the extremely varied decoherence behavior and the universal features of objectivity, promote the emergence of classicality and objective properties to a new and promising theory-independent line of research.
Research Interests:
We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated entirely in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them... more
We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated entirely in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically appealing. Again equivalently, they are stated in process-theoretic terms, establishing the fact that the conceptual bare-bones of quantum theory concerns the manner in which systems and processes compose. Aside from the diagrammatic form, the key novel aspect of this reconstruction is the introduction of a new postulate, symmetric purification. Unlike the ordinary purification postulate, symmetric purification applies equally well to classical theory as well as quantum theory. We therefore first reconstruct the full process theoretic description of quantum theory, consisting of composite classical-quantum systems and their interactions, before restricting ourselves to just the `fully quantum' systems in a final step. We propose two novel alternative manners of doing so, `no-leaking' (roughly that information gain causes disturbance) and `purity of cups' (roughly the existence of entangled states). Interestingly, these turn out to be equivalent in any process theory with cups and caps. Additionally, we show how the standard purification postulate can then be seen as an immediate consequence of the symmetric purification postulate and purity of cups. Other tangential results concern the specific frameworks of generalised probabilistic theories (GPTs) and process theories (a.k.a.~CQM). Firstly, we provide a diagrammatic presentation of GPTs, which, henceforth, can now be subsumed under process theories. Secondly, we have now characterised necessary additional axioms for a process theory to correspond to the Hilbert space model, and in particular, that a `sharp dagger' is indeed the right choice of a dagger structure.
Research Interests:
We propose four information-theoretic axioms for the foundations of statistical mechanics in general physical theories. The axioms---Causality, Purity Preservation, Pure Sharpness, and Purification---identify a class of theories where... more
We propose four information-theoretic axioms for the foundations of statistical mechanics in general physical theories. The axioms---Causality, Purity Preservation, Pure Sharpness, and Purification---identify a class of theories where every mixed state can be modelled as the marginal of a pure entangled state and where every unsharp measurement can be modelled as a sharp measurement on a composite system. This class of theories, called sharp theories with purification, includes quantum theory both with complex and real amplitudes, as well as a suitable extension of classical probability theory where classical systems can be entangled with other, non-classical systems. Theories satisfying our axioms support well-behaved notions of majorization, entropy, and Gibbs states, allowing for an information-theoretic derivation of Landauer's principle. We conjecture that every theory admitting a sensible thermodynamics must be extendable to a sharp theory with purification.
Research Interests:
Microcanonical thermodynamics studies the operations that can be performed on systems with well-defined energy. So far, this approach has been applied to classical and quantum systems. Here we extend it to arbitrary physical theories,... more
Microcanonical thermodynamics studies the operations that can be performed on systems with well-defined energy. So far, this approach has been applied to classical and quantum systems. Here we extend it to arbitrary physical theories, proposing two requirements for the development of a general microcanonical framework. We then formulate three resource theories, corresponding to three different sets of basic operations: i) random reversible operations, resulting from reversible dynamics with fluctuating parameters, ii) noisy operations, generated by the interaction with ancillas in the microcanonical state, and iii) unital operations, defined as the operations that preserve the microcanonical state. We focus our attention on a class of physical theories, called sharp theories with purification, where these three sets of operations exhibit remarkable properties. Firstly, each set is contained into the next. Secondly, the convertibility of states by unital operations is completely characterised by a majorisation criterion. Thirdly, the three sets are equivalent in terms of state convertibility if and only if the dynamics allowed by theory satisfy a suitable condition, which we call unrestricted reversibility. Under this condition, we derive a duality between the resource theories of microcanonical thermodynamics and the resource theory of pure bipartite entanglement.
Research Interests:
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM... more
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM and OPTs have found successful application to a number of areas in quantum foundations and information theory: they present many similarities, both in spirit and in formalism, but they remain separated by a number of subtle yet important differences. We attempt to bridge this gap, by adopting a minimal number of operationally motivated axioms which provide clean categorical foundations, in the style of CQM, for the treatment of the problems that OPTs are concerned with.
Research Interests:
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and... more
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect occurring with unit probability on some state. For theories satisfying our four axioms, we show a constructive algorithm for diagonalizing every given state. The diagonalization result allows us to formulate a majorization criterion that captures the convertibility of states in the operational resource theory of purity, where random reversible transformations are regarded as free operations.
Research Interests:
In this article we propose a new relativistic paradox concerning the absorption of a photon by a hydrogen atom. We show that the actual cause of the paradox is one of the hypotheses of Bohr model; therefore, in order to solve the paradox,... more
In this article we propose a new relativistic paradox concerning the absorption of a photon by a hydrogen atom. We show that the actual cause of the paradox is one of the hypotheses of Bohr model; therefore, in order to solve the paradox, we have to move away from Bohr model. Our analysis is carried out only in the special relativistic framework, so we are not interested in giving a full quantum mechanical treatment of the problem. We derive some expressions for emission and absorption of photons by atoms, which are in perfect agreement with special relativity, although comparable to the classical Bohr formula with an excellent degree of approximation. Quite interestingly, these expressions are no more invariant under a global shift of energy levels, showing a breaking of classical "gauge invariance" of energy. We stress that, to the best of our knowledge, the present approach has never been considered in literature. At the end we will be able to solve the proposed paradox.
Research Interests:
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification... more
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement and exploit it to define entanglement measures in the general probabilistic framework. In addition, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).
Research Interests:
We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic... more
We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.
Research Interests:
In this thesis we study the informational underpinnings of thermodynamics and statistical mechanics. To this purpose, we use an abstract framework—general probabilistic theories—, capable of describing arbitrary physical theories, which... more
In this thesis we study the informational underpinnings of thermodynamics and statistical mechanics. To this purpose, we use an abstract framework—general probabilistic theories—, capable of describing arbitrary physical theories, which allows one to abstract the informational content of a theory from the concrete details of its formalism. In this framework, we extend the treatment of microcanonical thermodynamics, namely the thermodynamics of systems with a well-defined energy, beyond the known cases of classical and quantum theory. We formulate two requirements a theory should satisfy to have a well-defined microcanonical thermodynamics. We adopt the recent approach of resource theories, where one studies the transitions between states that can be accomplished with a restricted set of physical operations. We formulate three different resource theories, differing in the choice of the restricted set of physical operations.
To bridge the gap between the objective dynamics of particles and the subjective world of probabilities, one of the core issues in the foundations of statistical mechanics, we propose four information-theoretic axioms. They are satisfied by quantum theory and more exotic alternatives, including a suitable extension of classical theory where classical systems interact with each other creating entangled states. The axioms identify a class of theories where every mixed state can be modelled as the reduced state of a pure entangled state. In these theories it is possible to introduce well-behaved notions of majorisation, entropy, and Gibbs states, allowing for an information-theoretic derivation of Landauer's principle. The three resource theories define the same notion of resource if and only if, on top of the four axioms, the dynamics of the underlying theory satisfy a condition called “unrestricted reversibility”. Under this condition we derive a duality between microcanonical thermodynamics and pure bipartite entanglement.
To bridge the gap between the objective dynamics of particles and the subjective world of probabilities, one of the core issues in the foundations of statistical mechanics, we propose four information-theoretic axioms. They are satisfied by quantum theory and more exotic alternatives, including a suitable extension of classical theory where classical systems interact with each other creating entangled states. The axioms identify a class of theories where every mixed state can be modelled as the reduced state of a pure entangled state. In these theories it is possible to introduce well-behaved notions of majorisation, entropy, and Gibbs states, allowing for an information-theoretic derivation of Landauer's principle. The three resource theories define the same notion of resource if and only if, on top of the four axioms, the dynamics of the underlying theory satisfy a condition called “unrestricted reversibility”. Under this condition we derive a duality between microcanonical thermodynamics and pure bipartite entanglement.
Research Interests:
Research Interests:
Since the early works of Einstein-Podolsky-Rosen and Schrödinger, entanglement is universally considered one of the most distinctive and puzzling features of quantum mechanics. In traditional introductions to the topics, entanglement is... more
Since the early works of Einstein-Podolsky-Rosen and Schrödinger, entanglement is universally considered one of the most distinctive and puzzling features of quantum mechanics. In traditional introductions to the topics, entanglement is presented as a consequence of the linear structure of the Hilbert space, which imposes that composite systems must have some pure states - the “entangled states” - that are not the product of pure states of the component systems. But is entanglement just a mathematical accident of the linearity of quantum mechanics, or perhaps a more fundamental feature related to the physical content of the theory? This thesis aims at giving a characterization of entanglement and of the transformations of entangled states only in terms of basic information-theoretic principles, without appealing to the specific details of the Hilbert space formalism of quantum mechanics. The principles used in this characterization provide a new angle on the foundations of thermodynamics, on the definition of entropic quantities, and on the relations between thermodynamics and information theory.
Research Interests:
Published in 1676 in London, the Neapolitan composer’s sixty-nine short pieces are grouped together in twelve suites, the second volume
Research Interests:
Published in 1676 in London, the Neapolitan composer’s sixty-nine short pieces are grouped together in twelve suites, the first volume.