Optical nonclassicality test based on third-order intensity correlations

We develop a nonclassicality criterion for the interference of three delayed, but otherwise identical, light fields in a three-mode Bell interferometer. We do so by comparing the prediction of quantum mechanics with those of a classical framework in which independent sources emit electric fields with random phases. In particular, we evaluate third-order correlations among output intensities as a function of the delays, and show how the presence of a correlation revival for small delays cannot be explained by the classical model of light. The observation of a revival is thus a nonclassicality signature, which can be achieved only by sources with a photon-number statistics that is highly sub-Poissonian. Our analysis provides strong evidence for the nonclassicality of the experiment discussed in [Menssen et al., PRL, 118, 153603 (2017)], and shows how a collective "triad" phase affects the interference of any three or more light fields, irrespective of their quantum or classical character

Versatile relative entropy bounds for quantum networks

We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of Azuma et al (2016 Nat. Commun. 7 13523) of splitting the network into two parts, our approach relaxes their strong restriction, consisting of the use of a single entanglement measure in the quantification of the maximum amount of entanglement generated by the channels. In particular, in our bound the measure can be chosen on a channel-by-channel basis, in order to make it as tight as possible. This enables us to apply the relative entropy of entanglement, which often gives a state-of-the-art upper bound, on every Choi-simulable channel in the network, even when the other channels do not satisfy this property. We also develop tools to compute, or bound, the max-relative entropy of entanglement for channels that are invariant under phase rotations. In particular, we present an analytical formula for the max-relative entropy of entanglement of the qubit amplitude damping channel

Gaussian discriminating strength

We present a quantifier of non-classical correlations for bipartite, multi-mode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in A. Farace et al., New. J. Phys. 16, 073010 (2014). As the latter the new measure exploits the Quantum Chernoff Bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam-splitter a factorized two-mode thermal state. For these density matrices, we study how non-classical correlations are related with the entanglement present in the system and with its total photon number

Discriminating strength: a bona fide measure of non-classical correlations

A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state \rho of a composite system AB as a probe for a quantum illumination task [e.g. see S. Lloyd, Science 321, 1463 (2008)], in which one is asked to remotely discriminate among the two following scenarios: i) either nothing happens to the probe, or ii) the subsystem A is transformed via a local unitary R_A whose properties are partially unspecified when producing \rho. This new measure can be seen as the discrete version of the recently introduced Intereferometric Power measure [G. Girolami et al. e-print arXiv:1309.1472 (2013)] and, at least for the case in which A is a qubit, it is shown to coincide (up to an irrelevant scaling factor) with the Local Quantum Uncertainty measure of D. Girolami, T. Tufarelli, and G. Adesso, Phys. Rev. Lett. 110, 240402 (2013). Analytical expressions are derived which allow us to formally prove that, within the set of separable configurations, the maximum value of our non-classicality measure is achieved over the set of quantum-classical states (i.e. states \rho which admit a statistical unravelling where each element of the associated ensemble is distinguishable via local measures on B)