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Genuine Quantumness in Cooperative Phenomena

Periodic Reporting for period 4 - GQCOP (Genuine Quantumness in Cooperative Phenomena)

Reporting period: 2019-11-01 to 2020-10-31

The project GQCOP addressed issues of fundamental and technological importance in quantum information science and its interplay with complexity. This project was driven by the scientific curiosity to explore the ultimate range of applicability of quantum mechanics and to develop novel platforms for the practical utilisation of quantum resources in technology applications. This programme had five specific objectives:

O1. Constructing a quantitative theory of quantumness in composite systems;
O2. Benchmarking genuine quantumness in information and communication protocols;
O3. Devising practical solutions for quantum-enhanced metrology in noisy conditions;
O4. Developing quantum thermal engineering for refrigerators and heat engines;
O5. Establishing a cybernetics framework for regulative phenomena in the quantum domain.
In this project, we unearthed, pushed, and recharted the boundaries of the quantum world. On one hand, this shed new light on fundamental aspects of quantum theory, by unveiling its signatures in systems of increasing complexity. On the other hand, this led to novel blueprints for practical quantum technologies, able to operate in real world conditions. The project produced over 100 publications. Our research impacted not only on the scientific community – opening new directions in quantum science – but also on policymakers and general public – inspiring them through press releases, visual arts, poetry, and interventions at World Economic Forum meetings.

MAIN ACHIEVEMENTS

O1:
We developed fundamental contributions to the characterisation of quantum coherence and all forms of quantum correlations. We established general "monogamy" limitations on the shareability of such correlations. We developed efficient schemes to witness and estimate signatures of quantumness in systems of arbitrary dimension without the need for a complete tomographical reconstruction of the quantum state. We resolved the longstanding debate about the nature of entanglement between identical particles by showing that the latter is a consistent physical resource. These results were corroborated by experimental demonstrations with photonics, ultracold atoms, and nuclear magnetic resonance setups.

O2:
We determined the maximum achievable performance of continuous variable quantum teleportation and quantum cryptography schemes using Gaussian states and operations. We provided the first unconditional security proof for the multipartite cryptographic primitive known as quantum secret sharing. We discovered that to achieve secure quantum teleportation with fidelity above the so-called no-cloning threshold one needs to exploit steering, a type of quantum correlation stronger than entanglement. We demonstrated experimentally the creation and distribution of steering in multimode states of light, and determined the best use of limited resources (energy and entanglement) for quantum communication.

O3:
We determined optimal strategies for noisy quantum metrology in discrete and continuous variable systems. We demonstrate the role of entanglement versus more general quantum correlations in providing quantum-enhanced measurements. We determined the ultimate limits on quantum superresolution imaging in three dimensions and investigated applications to surface metrology, with impact on the manufacturing industry. We developed novel mathematical techniques to evaluate the figure of merit accounting for the achievable precision in the estimation of multiple physical parameters.

O4:
We contributed to the expeditious development of quantum thermodynamics, through a series of organised events, an edited book which is now regarded as the primary reference in the field, and a number of seminal publications. These include the determination of universal performance bounds for autonomous quantum refrigerators, the establishment of fundamental limitations on algorithmic cooling with Gaussian operations, a complete classification of Gaussian thermal operations, the quantification of work extraction in assisted scenarios, and the proposal of experimentally feasible schemes for non-destructive thermometry of ultra-cold gases with individual quantum probes.

O5:
We applied notions inspired by cybernetics to the study and manipulation of quantum coherence, deriving fundamental fluctuation relations akin to the second law of thermodynamics. We quantified the usefulness of quantum correlations in quantum feedback cooling schemes. We established fundamental “no-go” limitations on distillation of Gaussian resources. We provided universal bounds on the emergence of objectivity of observables in quantum Darwinism for systems of arbitrary complexity. Last but not least, we demonstrated that every convex quantum resource yields an operational advantage in discrimination tasks, thus establishing the universal value of quantumness.
The research conducted in the ERC project has reached substantially beyond the state of the art, in particular in the theoretical characterisation and practical applications of general quantum resources. The contributions to the resource theory of quantum coherence have been far more substantial than originally planned in the proposal, eventually resulting in the definition of the first bona fide and operational measure of quantum coherence (robustness of coherence). These results have then been extended to arbitrary quantum resources, providing the first universal framework for their operational interpretation in terms of quantum discrimination tasks: This project has established that "every quantum helps", a result which has inspired numerous other studies even beyond quantum mechanics and that has been celebrated one of the most accomplished achievement in (quantum) resource theories.

The insights acquired in the context of the grant have consolidated the PI’s team into a position of leading expertise in quantum resources and quantum information theory. This has also led to three already highly cited review articles, one on quantum correlations, another on quantum coherence, and another on quantum metrology. The project also contributed to reshape the burgeoning field of quantum thermodynamics, pushing the boundaries of existing knowledge at the interface between open quantum systems, statistical mechanics, and information theory; these recent developments are summarised in a book with contributions from over a hundred international experts, co-edited by the PI and his team.

The project further reached towards the extremal and most elusive boundaries of the quantum world, both for what concerns the quantum-to-classical transition, which has been tracked under the quantitative lens of quantum Darwinism, and for what regards post-quantum and generalised probabilistic theories, in which the concept of entanglement has been rigorously formalised at the end of this project. All of these developments go beyond the state of the art and even beyond the initial expected outcomes of the project.

The research conducted in this project can be regarded as the compilation of a "recipe book" for the delivery of novel efficient quantum technologies exploiting quantum correlations and coherence as a resource, in particular in the context of quantum discrimination and metrology. These are expected to revolutionise information processing and communication as well as many commercial sectors in the next decades.
The robustness of coherence quantifies the quantum advantage in phase discrimination tasks
Hierarchy of correlations in composite quantum systems