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Non-locality in Multipartite Quantum Systems

Periodic Reporting for period 1 - N-MuQuaS (Non-locality in Multipartite Quantum Systems)

Reporting period: 2016-04-01 to 2018-03-31

Local measurements on composite quantum systems can lead to correlations that cannot be explained by any means known to classical physics. This phenomenon, known as non-locality, not only shows that quantum and classical worlds dramatically depart one from another at the micro scale, but more importantly, serves as a powerful resource for interesting applications. In fact, non-locality lies at the heart of device-independent quantum information processing, a new paradigm for information processing aiming at designing protocols which do not rely on any assumptions on the devices used. Detection of non-locality and its characterization in composite quantum systems is one of the key problems in quantum information theory and central to the possibility of its full exploitation as a resource. In particular, the studies of non-locality in multipartite quantum systems are much less advanced than in the bipartite ones. An additional, though equally important, motivation to study multipartite systems is the recent progress in experimental realization of various many-body quantum states creating a platform for experimental implementation of theoretical predictions.

The overall aim of this project was therefore to significantly improve our understanding of the phenomenon of non-locality in multipartite quantum systems. The project was structured around three sub-projects, each defining more concrete objectives.
First, we aimed at understanding the relation between non-locality and entanglement—another key notion in quantum information—in the multipartite scenario. The second aim was to design methods of detection of non-locality in the multipartite scenario with the aid of quantities that are within reach of current experimental technology, and also to explore the phenomenon of non-locality in many-body interacting quantum systems. Finally, we aimed at addressing a more fundamental problem, that is, to propose information-theoretic principles allowing to single out the set of quantum correlations from the nonsignaling ones.

As for the first aim, we have provided a general construction of multipartite quantum states that are genuinely entangled but not genuinely non-local, thus showing that the inequivalence between entanglement and non-locality is a more generic feature of multipartite quantum systems than we thought. As for the second aim, we have introduced a general toolbox for studying non-locality in one-dimensional many-body interacting quantum systems with the aid of few-body correlations; within this approach the energy of a quantum many-body system can tell us whether it is non-local. We have also shown how the number of particles sharing genuine non-locality in a multipartite system can be certified from only two-body correlations. Finally, we have constructed a general class of Bell inequalities, involving an arbitrary number of measurements and outcomes, which are maximally violated by the maximally entangled states and provided numerical evidence that these inequalities can be used for self-testing.
Within the first part of the project we have designed a method allowing one to map bipartite entangled states to the multipartite scenario, which yields states that are genuinely entangled, but not genuinely non-local. We have thus obtained a construction of quantum states featuring inequivalence between the notions of entanglement and non-locality in the multipartite scenario. In order to reach this goal we have also studied subspaces of multipartite Hilbert spaces that are void of any type of product vectors and provided constructions thereof.

In the second part of the project we have established a link between quantum many-body systems and non-locality. We have introduced a method allowing one to reveal non-locality of low-energy states of one-dimensional many-body interacting quantum systems with the aid of quantities that are measurable in current experiments. On the other hand, we have pointed out that tools frequently used to study quantum many-body systems can be harnessed to study Bell inequalities, in particular to efficiently compute the maximal classical and quantum values thereof. We have also provided a construction of Bell-like inequalities capable of revealing entanglement depth in multipartite quantum states.

Finally, in the third part of the project, among other, we have constructed and fully characterized a class of Bell inequalities involving arbitrary numbers of measurements and outcomes whose maximal quantum violation is achieved on the maximally entangled states. We have also pointed out certain device-independent applications of our Bell inequalities such as for instance self-testing. Interestingly, violation of these inequalities have been tested on entangled states generated in an experiment involving a large-scale integrated photonic quantum chip.

Each of the above accomplishments has involved extensive international collaboration with different European institutions and has lead to independent well-received scientific publications, all of them freely accessible online and many of them already published in renowned physical journals. Moreover, thanks to the fellowship the results obtained during the action have been presented on scientific events. Last but not least, I engaged in a variety of outreach and popularization activities.
At least three aspects should be taken into account when considering the impact of the fellowship. From the scientific point of view it has resulted in various interesting results, which are of relevance for our understanding of non-locality in composite quantum systems. The scientific output of the fellowship will also stimulate and inspire further research of this topic, both being crucial for full exploitation of non-locality as a resource in future quantum technologies. Second, the MSC fellowship allowed the researcher to maintain old and develop new scientific collaborations with top research centres in EU countries. At the same time, it enabled integration of the Researcher with one of the top institutes for theoretical physics in Poland, allowing to bring to Poland his experience and skills gained in other EU countries, all this being a key factor in the development and integration of the European society. Finally, and probably most importantly, the MSC fellowship was crucial for securing a permanent position at the research institute, allowing the Fellow to reach scientific maturity and helping him create his own group.
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