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Operational characterization of quantum correlations

Periodic Reporting for period 1 - OPERACQC (Operational characterization of quantum correlations)

Reporting period: 2015-05-01 to 2017-04-30

The peculiar kind of correlations that quantum systems can exhibit, and in particular quantum entanglement, is one of many aspects that differentiate quantum mechanics from classical mechanics. Such non-classical aspects are interesting both from a fundamental point of view and from a practical point of view. On one hand, we want to understand better how nature works, particularly going beyond our intuitive “classical” view of the world. On the other hand, non-classical properties can be exploited in quantum information processing (QIP) and quantum technologies.

The project aimed at characterizing and exploiting the quantum properties and behaviour – or, we will write in short, the “quantumness” – of correlated systems.

The project focused on obtaining a picture of quantum correlations and quantumness as unified and as operational as possible. By “operational” picture, we mean in particular that we aimed at characterizing quantum properties in terms of tasks for which quantum properties allow, e.g. to outperform the corresponding “classical” case, and in ways that may lead to direct and accessible experimental verification. Specifically, the project was based on the following three main approaches to the characterization of correlations:
- The consideration of the role of quantum correlations in the discrimination of physical processes;
- The development of tool and concepts related to the expression of quantum states of bipartite systems in a standard form;
- The view of correlations as resources under appropriate limitations in their manipulation.
We also aimed at understanding and verifying quantum correlations in concrete physical scenarios, like the ones encountered in atomic physics and quantum optics.

The action successfully:
- Proved that, the more a bipartite state is entangled, the more useful is it in the discrimination of physical processes
- Developed conceptual and quantitative tools for the quantification of the degree of correlations present in a bipartite quantum state, as well as its usefulness for discriminating any two arbitrary physical evolutions; this was based on a standard and convenient decomposition of bipartite quantum states
- Developed conceptual and quantitative tools for the quantification of the entanglement of identical particles; this is in particular relevant for experiments dealing with either fermions or bosons
- Developed conceptual and quantitative tools, based on the task of phase discrimination, for the quantification of general quantum coherence
- Provided further evidence that quantum coherence and quantum entanglement are deeply interrelated concepts, and provided ways to map the study of the former into the latter, also considering a many-body scenario
- Investigated the role of energy in the discrimination of physical processes; we introduced quantifiers of how different two physical processes are that depend on the amount of energy at disposal for the verification of such a difference
- Developed tools for the quantification of a quantumness of correlations that is more general than entanglement
We have studied the restrictions in the distribution of quantum correlations, both from a static perspective (to what extent entanglement can exists between multiple parties) or a dynamical one (to what extent correlations can be redistributed). We found that entanglement measures seem to obey a trade-off between their ability to capture quantitatively the fact that a state is highly entangled and their ability to capture the monogamy of entanglement. We proved that one can quantify the quantumness of correlations in an efficient way by considering the limitation in the symmetric local redistribution of correlations.

We have developed numerical tools for the quantification of the entanglement of identical particles. We have generalized and made quantitative a previously known approach to the problem.

We have studied properties of a special decomposition of bipartite states known as operator Schmidt decomposition. We have defined measures of total correlations based on such a decomposition, about which a paper is in preparation. We have defined a “discrimination power” associated to a given bipartite state, that captures how well such bipartite probe-ancilla state can allow to discriminate two arbitrary quantum evolutions affecting only the probe. We proved that such a discrimination power strongly depends on properties of the operator Schmidt decomposition of the state.

We defined measures of distinguishability of quantum evolutions based on the energy at disposal to probe such physical processes. Such energy-based distinguishability measures allow to extend to infinite-dimensional systems QIP results valid for finite-dimensional systems.

We have developed a framework for the quantification and exploitation of quantum coherence, that is, of the possibility of preparing quantum systems in a quantum superposition of “classical states”, a possibility that is also at the basis of entanglement. We have tackled the problem by looking at coherence as a particular case of asymmetry, that is, of lack of invariance under certain symmetry transformations. We quantified asymmetry and coherence by means of their robustness, that is, of the level of noise needed to destroy such resources. We have explored and developed a connection between entanglement and coherence, particularly in the case of multipartite entanglement and multilevel coherence. Multilevel coherence is also the topic of two other papers in preparation, one in collaboration also with experimentalists at the Heriot-Watt University in Edinburgh, and another purely theoretical one that focuses on the calculation of multilevel coherence for pure quantum states.

We have studied how the ignorance about an absolute reference frame for position or speed affects the entanglement between massive particles. In doing so, we have clarified the connection between difference approaches to dealing with the lack of such an absolute reference frame.

Besides publications in international peer-reviewed journals (including three articles in Physical Review letters), and several papers at the pre-print stage or in preparation, the results of the action have been disseminated also through the participation in international conferences and workshops, and through invited talks at external institutions. Some of the results have also been covered by news outlets like Phys.org and the Daily Mail.
The results obtained are internationally leading in the area of the study of entanglement, of general quantum correlations – also beyond entanglement – and of coherence.

Highlights of the progress beyond the state of the art include: we have shed light on the key property of entanglement monogamy; we have pointed out applications in communication and phase estimation that pin down quantitatively quantum coherence; we have developed new conceptual and quantitative tools for the estimation and discrimination of physical processes.

Our results are particularly relevant in the areas of quantum metrology and quantum communication. Applications of quantum metrology go from sensing to the development of more precise compact clocks. Applications of quantum communication go from extremely secure cryptography, to the realization of a future quantum internet.
A general quantumness of correlations can be characterized by local broadcasting.
Evolutions can be distinguished by making use of correlations between a probe and a reference
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