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Entanglement and Einstein–Podolsky–Rosen (EPR) steering are nonlocal quantum correlations, which are relevant resources for quantum information protocols. EPR steering, or quantum steering, refers to the correlation where a party might ‘steer’, or modify, the state of another, which is spatially separated. Entanglement is a symmetric resource while steering is asymmetrical, since it depends on the direction of the effect. Due to these different characteristics and the therefore different possible applications, there has been both theoretical and experimental research on forms to certify the distinct quantum nonlocal correlations. In recent years, alongside the investigation on quantum correlations between two systems, there has been a great interest in investigating multipartite/multimode entanglement as well as steering, since they include a high dimension and it may be possible to store more information than in a single qubit. In this review, we will summarize the different criteria and measures that have been developed for the characterization of these two kinds of correlations. We first focus on bipartite entanglement and steering. We then review the progress that has been made in the investigation of multipartite quantum correlations. We revise the theoretical work in quantum nonlocal correlation witnesses and measures, which respectively allow one to certify that the system is entangled or presents EPR steering, and give a quantification of the content of these correlations in the system. Then, we briefly review the experiments that have been designed and that demonstrate multipartite quantum correlations. We also include applications in quantum information protocols, in particular in quantum teleportation and quantum cryptography.

We investigate the violation of nonlocal realism using various entangled continues- and hybrid-variable states under dichotomic observables. In particular, we consider two cases of dichotomic observables (1) described by a pseudospin operator and (2) given in terms of the Wigner representation of the state in phase space, parity measurement and displacement operation. We address the recently proposed operational measure of nonlocality which describes the probability of local-realism violation under randomly sampled observables. We show the usefulness and limitations of the probability of local-realism violation for the detection of nonlocality. A simple procedure to detect such nonlocal correlations for randomly chosen settings with efficiencies of up to 100% is proposed. The practical advantage of applying random measurements that considerably lowers the experimental requirements is mentioned.

As a precious global resource in quantum information, genuine tripartite nonlocality (GTN) can be quantified by violating Svetlichny inequality. However, there is still no analytical expression for the general three-qubit states due to the difficulty of theoretical calculations. In this paper, we numerically achieve highly accurate quantization of GTN for GHZ-class states, and this method is also applicable to any three-qubit states. As an example, we study the dynamics of GTN and genuine tripartite entanglement (GTE) for the W state. Moreover, the complementarity of GTN is verified by examining the nonlocality between the tripartite and the bipartite states. Finally, we also find a useful strategy to protect the correlation of GTN and GTE under decoherence by utilizing the Zeno effect.

In the paper, we devote to defining an available measure to quantify the nonbilocal correlation in the entanglement-swapping experiment. Then we obtain analytical formulas to calculate the quantifier when the inputs are pure states. For the case of mixed inputs, we discuss the computational properties of the quantifier. Finally, we derive a tight upper bound to the nonbilocality quantifier.

A key open issue in condensed-matter physics is how quantum and classical correlations emerge in an unconventional superconductor from the underlying normal state. We study this problem in a doped Mott insulator with information-theory tools on the two-dimensional (2D) Hubbard model at finite temperature with cluster dynamical mean-field theory. We find that the local entropy detects the superconducting state and that the difference in the local entropy between the superconducting and normal states follows the same difference in the potential energy. We find that the thermodynamic entropy is suppressed in the superconducting state and monotonically decreases with decreasing doping. The maximum in entropy found in the normal state above the overdoped region of the superconducting dome is obliterated by superconductivity. The total mutual information, which quantifies quantum and classical correlations, is amplified in the superconducting state of the doped Mott insulator for all doping levels and shows a broad peak versus doping, as a result of competing quantum and classical effects.

We present a solid-state nuclear magnetic resonance (NMR) spectroscopy study of the local 31 P and 1 H environments in monetite [CaHPO 4 ; dicalcium phosphate anhydrous (DCPA)], as well as their relative spatial proximities. Each of the three 1 H NMR peaks was unambiguously assigned to its respective crystallographically unique H site of monetite, while their pairwise spatial proximities were probed by homonuclear 1 H– 1 H double quantum–single quantum NMR experimentation under fast magic-angle spinning (MAS) of 66 kHz. We also examined the relative 1 H– 31 P proximities among the inequivalent P1, P2 and H1, H2, H3 sites in monetite; the corresponding shortest internuclear 1 H– 31 P distances accorded well with those of a previous neutron diffraction study. The NMR results from the monetite phase were also contrasted with those observed from the monetite component present in a pyrophosphate-bearing calcium phosphate cement, demonstrating that while the latter represents a disordered form of monetite, it shares all essential local features of the monetite structure.

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10⁷) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry–Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to −2.4 dB (−3.6 dB if corrected for detection losses) and bandwidths <90 kHz. The multimode nature of the membrane and Fabry–Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.

Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.

The benefits of entanglement can outlast entanglement itself. In quantum illumination, entanglement is employed to better detect reflecting objects in environments so noisy that all entanglement is destroyed. Here, we show that quantum discord-a more resilient form of quantum correlations-explains the resilience of quantum illumination. We introduce a quantitative relation between the performance gain in quantum illumination and the amount of discord used to encode information about the presence or absence of a reflecting object. This highlights discords role preserving the benefits of entanglement in entanglement breaking noise.

In this paper, we investigate the possibility of explaining nonclassical correlations between two quantum systems in terms of quantum interferences between collective states of the two systems. We achieve this by mapping the relations between different measurement contexts in the product Hilbert space of a pair of two-level systems onto an analogous sequence of interferences between paths in a single-particle interferometer. The relations between different measurement outcomes are then traced to the distribution of probability currents in the interferometer, where paradoxical relations between the outcomes are identified with currents connecting two states that are orthogonal and should therefore exclude each other. We show that the relation between probability currents and correlations can be represented by continuous conditional (quasi)probability currents through the interferometer, given by weak values; the violation of the noncontextual assumption is expressed by negative conditional currents in some of the paths. Since negative conditional currents correspond to the assignment of negative conditional probabilities to measurements results in different measurement contexts, the necessity of such negative probability currents represents a failure of noncontextual local realism. Our results help to explain the meaning of nonlocal correlations in quantum mechanics, and support Feynman’s claim that interference is the origin of all quantum phenomena.