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.
Highlights
An important guiding principle for quantum theorists is the identification of genuine nonclassical effects certified by rigorous theorems
We describe the operational features of optimal state-dependent quantum cloning which, as we will show, are impossible to explain with noncontextual models
We have shown that the operational statistics observed in the optimal state-dependent quantum cloning is incompatible with the predictions of every noncontextual ontological model
Summary
We can schematically think of an experiment as a set of black-boxes each corresponding to certain sets of operational instructions. We can distinguish three kinds of black-boxes: 1. A preparation black-box Ps initialises the system; 2. Two operational procedures (be them preparations, measurements or transformations) are said to be operationally equivalent if they cannot be distinguished by any experiment. Noncontextuality, in the generalized form introduced in [6], is a restriction to ontological models requiring that if two procedures are operationally equivalent, they must be represented by the same object in the ontological model. This notion can be seen as an extension of the traditional one of Kochen-Specker [6, 15]. Examples of noncontextual ontological models include classical Hamiltonian mechanics, Hamiltonian mechanics with a resolution limit on phase space [7] and Spekken’s toy model [8]
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