In this work, we extend known Kirkwood-Dirac (KD) quasiprobability distributions for states to any quantum process: channels, composite systems, and effects. In this way, we formally show that KD representations are formal quasiprobability models of any quantum process. Using this technical advancement, we also show that real nonnegative KD representations of a fragment of quantum theory correspond to ontological models for that fragment. And on the other hand, negativity/imaginarity is not enough, in general, to conclude contextuality.

In this work we show how the unitary-invariant toolbox of two-state overlap inequalities can also be used to witness magic inside quantum processing units (QPUs). This is the first protocol for witnessing magic that is semi-device independent, robust to any form of incoherent noise, and efficient to prove experimentally (in terms of number of measurements and samples). We introduce the notion of set magic, that allows for funny things such as distributing a certification across different QPUs. 

In this recent work, we investigate the possibility of witnessing quantum imaginarity using Bargmann invariants. Third-order Bargmann invariants can witness such resources whenever their imaginary parts are non-zero. We completely characterize the set of all possible values that these imaginary parts can have, for any possible 3 states and provide numerical evidence that we also have full characterization of the case of all 4 states as well (in any dimension). 

If one consider pure states, we show that it is impossible to witness imaginarity using pairwise two-state overlaps of 3 states, but for 4 states it is possible and we present a concrete experimental procedure for witnessing quantum imaginarity.

In this study, we experimentally certify contextuality, coherence, and the Hilbert space dimension of a 6-mode programmable universal photonic chip, which was constructed using state-of-the-art laser writing techniques. We employ a recently introduced infinite family of two-state overlap inequalities to assess the device's capabilities.

Our results demonstrate that these inequalities cannot be violated without sufficient access to the device's modes. Beyond that, they reveal the generation of highly non-trivial coherence. Additionally, we establish a quantum advantage in the context of quantum interrogation using these inequalities. Our findings not only confirm the device's ability to generate generalized contextuality, a high bar for nonclassical statistics, but also show its potential to use this resource for powering the interrogation task.

DOI: 10.1126/sciadv.adj4249 

We introduce an infinite family of extended Wigner's friend scenarios in which observers that make sequential measurements over a system S that reason about their outcomes are lead to contradictory/paradoxical reasonings. 

We use n-cycle logically contextual behaviours to generate such paradoxes. In doing so, we avoid the usage of any for of nonlocal correlations of the initial system. In the simplest case, a contradiction is obtained from measurements over a qutrit.

We introduce an infinite family of gadgets for cat states, injecting both non-Clifford and entangled unitaries fault-tolerantly in a given circuit. We study both magic and entanglement properties of cat states, and the optimality of the injection scheme. 

Later, we study the effectiveness of such states for classical simulation, quantum resource reduction, and to the generation of hardness of computation through the emergence of quantum information scrambling. We find that cat-state injection brings scrambling into initially separable Clifford circuits. We find also that although such cat states do not have an impact in standard classical simulation of quantum devices (as opposed to their usage in the ZX-calculus based simulation) they can be used to reduce quantum resources in general. 

We investigate the connection between weak values and nonclassicality from the point of view of quantum coherence. There have been a long standing debate questioning the nonclassicality present in anomalous weak values. This debate was settled after proofs that anomalous values arising from weak measurments cannot be explained by noncontextual ontological models.  Recently, it has been pointed out that weak values can be measured without strictly using the weak measurement scheme, without relying to quantum state tomography nor post-selection. We contributed in this novel way of testing weak values in the work below.

In our work we revisited a simple argument for the nonclassicality of anomalous values in terms of (basis-independent) coherence. Essentially, we show that any anomaly requires coherence of the pre/post selection states, regardless of purity, dimension of the physical system considered, and the specific eigenbasis of the observable in question, to be coherent. Moreover, we also study to what extent coherence is sufficient and we show that it is a very particular 'kind' of coherence that allows for anomalous weak values, namely, negativity, imaginarity, or anomaly of third-order Bargmann invariants. 

We use our results to claim that we can use modern techniques to witness generalized contextuality present in anomalous weak values without the necessity of the operational constraints relative to weak measurements. We also discuss how these results allow for robustly interpreting weak value statistics as witnesses of (basis-independent) coherence. (ArXiv version)

We describe how simple yet relevant quantum circuits can be used to measure weak values, Kirkwood-Dirac (KD) quasiprobabilities, and related quantities such as the out-of-time-ordered correlator and the post-selected quantum Fisher information. This is achieved by realizing that all of these quantities have a crucial common aspect: they are functions of unitary invariants called Bargmann invariants.

This simple connection has allowed us to present all of these circuits together, and we have realized that the nonclassicality in all of these quantities comes from a property that was recently introduced and described as set coherence. This novel notion of coherence characterizes coherence as a relational property of a set of states, and as such, it is immediately linked, from our perspective, to the advantages and all relevant uses of nonclassicality from the quantities mentioned before, in particular, weak values and KD distributions.

We apply the event graph ideas to study when it is possible to clearly witness nonclassicality inside interferometers. In many aspects, this kind of study might be relevant to characterization of photonic devices that are useful in proofs of quantum advantage. 

From this connection we are able also to describe a simple way for proving possible many new contextual advantages in protocols using coherence and superposition; as an example of this perspective we prove contextual advantage for the task of quantum interrogation.

It is unclear how the notion of coherence and contextuality are connected. It is unknown if coherence is necessary to contextuality -- as there are proofs of contextuality that are state-independent -- and there are also examples of toy models that are noncontextual while presenting coherence. 

In this work we are able to provide a new framework for witnessing coherence, nonlocality and contextuality using an inequalities paradigm. We show that those inequalities recover the entirety of all Kochen-Specker noncontextuality inequalities from the CSW approach, and also present generalized contextuality inequalities and the most famous inequalities such as the CHSH, KCBS, cycle-inequalities and simplest Bell inequality from the minimal scenario. This work marks a clear understanding between coherence and contextuality that was lacking, but also introduces a promissing paradigm due to its experimental and theoretical simplicity and its wide range of applicability.

The nascent field of quantum biology attempts at understanding what might be the role of quantum mechanics in many naturally occurring dynamical behaviors in biology. The most important of those, for technological and academic reasons, is the study of photosynthesis. 

In this work we study toy models of photosynthetic dynamics that depend on basis-dependent coherence. We study how varying many of the parameters in this dynamical system affect the success rates of energy transfer in general, and compare with values that are approximately close to photosynthetic systems.

Decoherence does not settle the debate on how objectivity, in the sense of observers that agree with each others results, emerges for macroscopic objects. The view of Quantum Darwinism is to promote the environment from a simple destructive agent of quantum information -- as it is in decoherence theory -- to the active agent selecting information to be 'proliferated' and to be available to be extracted by many observers. 

We connect this notion of emergence of objectivity with a solid notion of nonclassicality: generalized noncontextuality. This notion encompasses classical mechanics and is motivated by many philosophical desiderata that are also well-motivated from a purely classical world-view. We show then that Quantum Darwinism, when successful, destroys any generalized contextuality that could be present in a quantum system!

To the date of presentation of this work there was a single formal resource theory to study generalized contextuality, the one introduced by Barbara Amaral and Christiano Duarte (Recently, there is a new RT being introduced, but within the perspective of studying this notion of nonclassicality in the GPT framework). 

We use this RT to formally understand when we can witness and even engineer generalized contextuality, using an introduced notion of composing PM scenarios as well as simply re-thinking the effect of post-processing data-tables (behaviours). 

There are many non-equivalent ways to define what can be understood by contextuality. For each such a perspective, there are different approaches to understand notion. For example, the Kochen-Specker notion of contextuality can be studied using various graph-approaches, or the sheaf-approach; generalized contextuality can be studied using a GPT perspective or an OPT perspective and CbD might be studied using standard random variables data-tables or causal models based on latent variables (M-contextuality).

In this work we analyse how to approach the CbD 1.0 formalism from the perspective of behaviours instead of random variables. We connect the two ideas concretely and present the topic of CbD 1.0.