Construction of a structure which makes it possible to describe the joint system of a classical and a quantum system

Dirk Aerts

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers

Saikat Guha

Attaining the ultimate (Holevo) limit to the classical capacity of a quantum channel requires the receiver to make joint measurements over long code-word blocks. For a pure-state channel, we show that the Holevo limit can be attained by a receiver that uses a multisymbol unitary transformation on the quantum code word followed by separable projective measurements. We show a concatenated coding and joint-detection architecture to approach the Holevo limit. We then construct some of the first concrete examples of codes and structured joint-detection receivers for the lossy bosonic channel, which can achieve fundamentally higher (superadditive) capacity than conventional receivers that detect each modulation symbol individually. We thereby pave the way for research into codes and structured receivers for reliable communication data rates approaching the Holevo limit.

Omar Gamel, Graham R. Fleming

It is well known that noncommuting observables cannot be simultaneously measured in quantum theory. However, under hidden variable models, such observables must simultaneously hold premeasurement values. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fr\'echet bounds, finding that the joint probabilities may be negative. We then use the symmetrization heuristic to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct generalized Bell inequalities with a quantum to classical violation of \frac{3}{2}. The result demonstrates the importance of noncommutativity in the nonclassicality of quantum mechanics. However, the additional symmetrization assumption makes its conclusions weaker than traditional Bell inequalities.

Giacomo Mauro D’Ariano, Giulio Chiribella, Paolo Perinotti

In this chapter we introduce the principle of local discriminability, which stipulates the possibility of discriminating states of composite systems via local measurements on the component systems. The phenomenon of entanglement has relevant consequences on the accessibility of information in composite systems and on the complexity of characterization of transformations: local discriminability brings dramatic simplifications to the structure of the sets of states and transformations, reconciling the holism of entangled states with the reductionist scientific approach. In order to illustrate the structural relevance of the principle, we will briefly review some OPTs that do not satisfy it, contrasting the features of such theories with those of quantum and classical probabilistic theories, where the principle holds. Entanglement and Holism Holism is a widely known feature of quantum theory, related to the existence of entangled states. In quantum theory one has pure entangled states, whose marginal states are completely mixed. This situation corresponds to having maximal knowledge of the whole with minimal knowledge of the parts. The main manifestation of the holism of entanglement is the impossibility of reconciling the statistics of joint measurements on entangled states with local realism . Local realism is the assumption that any measurement on a system is just the reading of a pre-existing quantity encoded on the system. In other words, we cannot explain the statistics of measurements on the parts of a composite system as a manifestation of our ignorance of locally pre-existing values, as in classical OPT. Does entanglement make information about composite systems locally unaccessible? This would pose severe practical issues on the possibility of acquiring information about physical systems. For example, suppose that two distant telescopes observe a source of entangled photons from a stellar emission. Holism would imply that some features of the emission process could never be detected, unless we are able to make the entangled photons interact in a joint measurement. On the other hand, if a reductionist approach is possible, local observations of the two photons at the sites of the two telescopes would be enough to characterize the emitting source. Thanks to the local discriminability principle, this is actually the case with entangled quantum sources. Another consequence of holism is the fact that transformations generally cannot be characterized by local experiments, namely by applying the unknown transformation only to its input system.