Fundamental limits on concentrating and preserving tensorized quantum resources

Quantum technology offers great advantages in many applications by exploiting quantum resources like nonclassicality, coherence, and entanglement. In practice, an environmental noise unavoidably affects a quantum system and it is thus an important issue to protect quantum resources from noise. In this work, we investigate the manipulation of quantum resources possessing the so-called tensorization property and identify the fundamental limitations on concentrating and preserving those quantum resources. We show that if a resource measure satisfies the tensorization property as well as the monotonicity, it is impossible to concentrate multiple noisy copies into a single better resource by free operations. Furthermore, we show that quantum resources cannot be better protected from channel noises by employing correlated input states on joint channels if the channel output resource exhibits the tensorization property. We address several practical resource measures where our theorems apply and manifest their physical meanings in quantum resource manipulation.Comment: 12 pages, 3 figure

Toward correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game

Correlation self-testing of a theory addresses the question of whether we can identify the set of correlations realisable in a theory from its performance in a particular information processing task. Applied to quantum theory it aims to identify an information processing task whose optimal performance is achieved only by theories realising the same correlations as quantum theory in any causal structure. In [Phys. Rev. Lett. 125 060406 (2020)] we introduced a candidate task for this, the adaptive CHSH game. Here, we analyse the maximum probability of winning this game in different generalised probabilistic theories. We show that theories with a joint state space given by the minimal or the maximal tensor product are inferior to quantum theory, before considering other tensor products in theories whose elementary systems have various two-dimensional state spaces. For these, we find no theories that outperform quantum theory in the adaptive CHSH game and prove that it is impossible to recover the quantum performance in various cases. This is the first step towards a general solution that, if successful, will have wide-ranging consequences, in particular, enabling an experiment that could rule out all theories in which the set of realisable correlations does not coincide with the quantum set.Comment: 12+2 pages, 2 figures; v2: typos correcte

Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular causal structure, namely, one wherein the wings are only connected by a common cause. We term them "common-cause boxes". We define the distinction between classical and nonclassical resources in terms of whether or not a classical causal model can explain the correlations. One can then quantify the relative nonclassicality of resources by considering their interconvertibility relative to the set of operations that can be implemented using a classical common cause (which correspond to local operations and shared randomness). We prove that the set of free operations forms a polytope, which in turn allows us to derive an efficient algorithm for deciding whether one resource can be converted to another. We moreover define two distinct monotones with simple closed-form expressions in the two-party binary-setting binary-outcome scenario, and use these to reveal various properties of the pre-order of resources, including a lower bound on the cardinality of any complete set of monotones. In particular, we show that the information contained in the degrees of violation of facet-defining Bell inequalities is not sufficient for quantifying nonclassicality, even though it is sufficient for witnessing nonclassicality. Finally, we show that the continuous set of convexly extremal quantumly realizable correlations are all at the top of the pre-order of quantumly realizable correlations. In addition to providing new insights on Bell nonclassicality, our work also sets the stage for quantifying nonclassicality in more general causal networks.Comment: V4 changes: Accepted by Quantum, bibliography hyperlinks adjusted according to journal policy. Slight reorganization of content in Section