Contextual advantage for state-dependent cloning

Abstract

A number of noncontextual models exist which reproduce different subsets of quantum theory and admit a no-cloning theorem. Therefore, if one chooses noncontextuality as one's notion of classicality, no-cloning cannot be regarded as a nonclassical phenomenon. In this work, however, we show that there are aspects of the phenomenology of quantum state cloning which are indeed nonclassical according to this principle. Specifically, we focus on the task of state-dependent cloning and prove that the optimal cloning fidelity predicted by quantum theory cannot be explained by any noncontextual model. We derive a noise-robust noncontextuality inequality whose violation by quantum theory not only implies a quantum advantage for the task of state-dependent cloning relative to noncontextual models, but also provides an experimental witness of noncontextuality.An important guiding principle for quantum theorists is the identification of genuine nonclassical effects certified by rigorous theorems. Given a quantum phenomenon, the relevant question is: Are there classical models able to reproduce the observed operational data? Here we investigate this question in the context of a cloning experiment.

Teoria de recursos para contextualidade generalizada

“…, which is related to the l 1 -distance monotone d. The RHS is the l 1 -norm over the ontological quantities that are of importance for proving noncontextual bounds for quantum cloning, see (Lostaglio and Senno, 2020), and quantum state discrimination, see . This induces us to speculate that the operational quantity d could provide bounds for the ontological description of the epistemic states, which in itself might represent a clue for increasing our understanding of scenarios with preparation contextuality.…”

“…It might be simply a unreasonable trick to create nonclassicality by force: Criticism in this spirit leads to completely new attempts to even define noncontextuality. But we would like to make the following interpretation (Lostaglio and Senno, 2020): let Pφ be a preparation procedure such that, p(φ|M φ , Pφ) = 0 (5.31)…”

“…There is still much work towards a full comprehension of how, when and why we can consider the relationship between transformation procedures and prepare-and-measure scenarios. The paper of (Lostaglio and Senno, 2020) is one of the attempts to study such a situation. Another one that deals with anomalous weak values and that it is interesting for quantum thermodynamics is the study presented in (Kunjwal et al, 2019).…”

“…This operational scenario described in the terms of relates to the one in (Lostaglio and Senno, 2020) via the following definition:…”

“…Definition 32. (Lostaglio and Senno, 2020) Let p(1|M aa , P α ) ≡ p aa,α be our notation for the conditional probabilities in the behaviors corresponding to the scenario B qc from definition 31. Then, the global cloning fidelity operationally defined is, F g : B qc → R + defined as,…”