Abstract
We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models, which will be defined in this work. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.
Highlights
We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone
Our framework provides an inherent post-quantum steering quantifier in terms of the minimal negativity of the operator rnecessary to reproduce a given assemblage. We prove that such a quantifier does not increase under processing of the assemblage by means of one-way quantum operations from the steered party to the steering party, whereas standard steering is postulated not to increase under one-way local operations and classical communication
While such an r ¢ may not be optimal for the sake of the steering negativity of the new assemblage, since the trace norm does not increase under the partial action of a completely positive and trace-preserving map, this is enough to prove that the steering negativity does not increase under processing by one-way quantum operations
Summary
By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. In this work we develop a framework for steering based on that of [19] (see [20]) for Bell non-locality In this formalism, the parties share a (potentially non-quantum) system in the (potentially unphysical) state r , where some parties steer the others by performing quantum measurements on their share of the system. We study assemblages that arise when the parties perform local measurements on entanglement witnesses constructed from an unextendible product basis [22] This is a simple construction that always yields certifiable post-quantum assemblages ( with post-quantum correlations).
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