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We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states. [ABSTRACT FROM AUTHOR]

The presence of quantum correlations in a quantum state is related to the stateʼs response to local unitary perturbations. Such a response is quantified by the distance between the unperturbed and perturbed states, minimized with respect to suitably identified sets of local unitary operations. In order to be a bona fide measure of quantum correlations, the distance function must be chosen among those that are contractive under completely positive and trace preserving (CPTP) maps. The most relevant instances of such physically well-behaved metrics include the trace, the Bures, and the Hellinger distance. To each of these metrics one can associate the corresponding discord of response, namely the trace, or Hellinger, or Bures minimum distance from the set of unitarily perturbed states. All these three discords of response satisfy the basic axioms for a proper measure of quantum correlations. In the present work we focus in particular on the Bures distance, which enjoys the unique property of being both Riemannian and contractive under CPTP maps, and admits important operational interpretations in terms of state distinguishability. We compute analytically the Bures discord of response for two-qubit states with maximally mixed marginals and we compare it with the corresponding Bures geometric discord, namely the geometric measure of quantum correlations defined as the Bures distance from the set of classical-quantum states. Finally, we investigate and identify the maximally quantum correlated two-qubit states according to the Bures discord of response. These states exhibit a remarkable nonlinear dependence on the global state purity. [ABSTRACT FROM AUTHOR]

In a single qubit system, a universal quantum classifier can be realized using the data reuploading technique. In this study, we propose a new quantum classifier applying this technique to bosonic systems and successfully demonstrate it using a silicon-based photonic integrated circuit. We established a theory of quantum machine learning algorithm applicable to bosonic systems and implemented a programmable optical circuit combined with an interferometer. Learning and classification using part of the implemented optical quantum circuit with uncorrelated two photons resulted in a classification with a success probability of 94±0.8% in the proof of principle experiment. As this method can be applied to an arbitrary two-mode N-photon system, further development of optical quantum classifiers, such as extensions to quantum entangled and multiphoton states, is expected in the future.

Proofs of the quantum advantage available in imaging or detecting objects under quantum illumination can rely on optimal measurements without specifying what they are. We use the continuous-variable Gaussian quantum information formalism to show that quantum illumination is better for object detection compared with coherent states of the same mean photon number, even for simple direct photodetection. The advantage persists if signal energy and object reflectivity are low and background thermal noise is high. The advantage is even greater if we match signal beam detection probabilities rather than mean photon number. We perform all calculations with thermal states, even for non-Gaussian conditioned states with negative Wigner functions. We simulate repeated detection using a Monte-Carlo process that clearly shows the advantages obtainable.

In this paper we present an evolution of the single-pixel camera architecture, called "pushframe," which addresses the limitations of pushbroom cameras in space-based applications. In particular, it is well-suited to observing fast-moving scenes while retaining high spatial resolution and sensitivity. We show that the system is capable of producing color images with good fidelity and scalable resolution performance. The principle of our design broadens the choice of spectral ranges that can be captured, making it suitable for wide spectral ranges of infrared imaging.

Boson sampling can simulate physical problems for which classical simulations are inefficient. However, not all problems simulated by boson sampling are classically intractable. We show explicit classical methods of finding boson sampling distributions when they are known to be highly sparse. In the methods, we first determine a few distributions from restricted number of detectors and then recover the full one using compressive sensing techniques. In general, the latter step could be of high complexity. However, we show that this problem can be reduced to solving an Ising model which under certain conditions can be done in polynomial time. Various extensions are discussed including a version involving quantum annealing. Hence, our results impact the understanding of the class of classically calculable problems. We indicate that boson samplers may be advantageous in dealing with problems which are not highly sparse. Finally, we suggest a hybrid method for problems of intermediate sparsity.

We investigate the dynamics of Gaussian states of continuous variable systems under Gaussianity-preserving channels. We introduce a hierarchy of such evolutions encompassing Markovian and weakly and strongly non-Markovian processes and provide simple criteria to distinguish between the classes, based on the degree of positivity of intermediate Gaussian maps. We present an intuitive classification of all one-mode Gaussian channels according to their non-Markovianity degree and show that weak non-Markovianity has an operational significance, as it leads to a temporary phase-insensitive amplification of Gaussian inputs beyond the fundamental quantum limit. Explicit examples and applications are discussed.

Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation of the phenomenon for noisy quantum technologies.

The mutual information between the sender of a classical message encoded in quantum carriers and a receiver is fundamentally limited by the Holevo quantity. Using strong subadditivity of entropy, we prove that the Holevo quantity is not larger than an exchange entropy. This implies an upper bound for coherent information. Moreover, restricting our attention to classical information, we bound the transmission distance between probability distributions by their entropic distance, which is a concave function of their Hellinger distance.