Genuine Multipartite Steering Research Articles

Probing Genuine Multipartite Einstein–Podolsky–Rosen Steering and Entanglement Under an Open Tripartite System

Einstein–Podolsky–Rosen steering is a peculiar quantum nonlocal correlation and has unique physical characteristics and a wide application prospect. Even more importantly, multipartite steerable states have more vital applications in the future quantum information field. Thus, in this work, we explored the dynamics characteristics of both genuine multipartite steering (GMS) and genuine multipartite entanglement (GME) and the relations of both under an open tripartite system. Specifically, the tripartite decoherence system may be modeled by the three parties of a tripartite state that undergo the noisy channels. The conditions for genuine entangled and steerable states can be acquired for the initial tripartite state. The results showed that decoherence noises can degrade the genuine multipartite entanglement and genuine multipartite steering and even induce its death. Explicitly, GME and GMS disappear with the increase in the decoherence strength under the phase damping channel. However, GME and GMS rapidly decay to death with the increase in the channel-noise factor and then come back to life soon after in the bit flip channel. Additionally, the results indicate that GMS is born of GME, but GME does not imply GMS, which means that the set of genuine multipartite steerable states is a strict subset of the set of genuine multipartite entangled states. These conclusions may be useful for discussing the relationship of quantum nonlocal correlations (GME and GMS) in the decoherence systems.

Multi-color quantum steering frequency comb produced by enhanced Raman scattering

A scheme is proposed to generate multi-color quantum steering frequency comb in a two-dimensional hexagonal-poled LiTaO3 crystal through enhanced Raman scattering. The quantum steering correlations among the Stokes and anti-Stokes Raman beams are demonstrated by applying the criteria for genuine multipartite steering. Multi-color quantum steering frequency comb generated in present scheme has potential application prospects in quantum information processing.

Full multipartite steering inseparability, genuine multipartite steering, and monogamy for continuous-variable systems

We derive inequalities sufficient to detect the genuine $N$-partite steering of $N$ distinct systems. Here, we are careful to distinguish between the concepts of full $N$-partite steering inseparability (where steering is confirmed individually for all bipartitions of the $N$ systems, thus negating the bilocal hidden state model for each bipartition) and genuine $N$-partite steering (which excludes all convex combinations of the bilocal hidden state models). Other definitions of multipartite steering are possible and we also derive inequalities to detect a stricter genuine $N$-partite steering where only one site needs to be trusted. The inequalities are expressed as variances of quadrature phase amplitudes and thus apply to continuous-variable systems. We show how genuine $N$-partite steerable states can be created and detected for the nodes of a network formed from a single-mode squeezed state passed through a sequence of $N\ensuremath{-}1$ beam splitters. A stronger genuine $N$-partite steering is created, if one uses two squeezed inputs or $N$ squeezed inputs. We are able to confirm that genuine tripartite steering (by the above definition and by the stricter definition) has been realized experimentally. Finally, we analyze how bipartite steering and entanglement are distributed among the systems in the tripartite case, illustrating with monogamy inequalities. While we use Gaussian states to benchmark the criteria, the inequalities derived in this paper are not based on the assumption of Gaussian states, which gives an advantage for quantum communication protocols.

Hierarchy of genuine multipartite quantum correlations

Classifying quantum states which exhibit different statistical correlations is among the most important problems in quantum information science and quantum many-body physics. In bipartite case, there is a clear hierarchy of states with different correlations: total correlation (T) \(\supsetneq \) discord (D) \(\supsetneq \) entanglement (E) \(\supsetneq \) steering (S) \(\supsetneq \) Bell nonlocality (NL). However, very little is known about genuine multipartite correlations (GM\(\mathcal {C}\)) for both conceptual and technical difficulties. In this work, we show that, for any N-partite qudit states, there also exists such a hierarchy: genuine multipartite total correlations (GMT) \(\supseteq \) genuine multipartite discord (GMD) \(\supseteq \) genuine multipartite entanglement (GME) \(\supseteq \) genuine multipartite steering (GMS) \(\supseteq \) genuine multipartite nonlocality (GMNL). Furthermore, by constructing explicit states, we show that GMT, GME and GMS are inequivalent with each other and thus GMT \(\supsetneq \) GME \(\supsetneq \) GMS.

Revealing genuine steering under sequential measurement scenario

Genuine steering is still not well understood enough in contrast to genuine entanglement and nonlocality. Here, we provide a protocol which can reveal genuine steering under some restricted operations compared to the existing witnesses of genuine multipartite steering. Our method has an impression of some sort of ‘hidden’ protocol in the same spirit of hidden nonlocality, which is well understood in bipartite scenario. We also introduce a genuine steering measure which indicates the enhancement of genuine steering in the final state of our protocol compared to the initial states.

Exploring Multipartite Steering Effect Using Bell Operators.

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.

Experimental verification of multidimensional quantum steering

Quantum steering enables one party to communicate with another remote party even if the sender is untrusted. Such characteristics of quantum systems not only provide direct applications to quantum information science, but are also conceptually important for distinguishing between quantum and classical resources. While concrete illustrations of steering have been shown in several experiments, quantum steering has not been certified for higher dimensional systems. Here, we introduce a simple method to experimentally certify two different kinds of quantum steering: Einstein–Podolsky–Rosen (EPR) steering and single-system (SS) steering (i.e., temporal steering), for dimensionality (d) up to d=16. The former reveals the steerability among bipartite systems, whereas the latter manifests itself in single quantum objects. We use multidimensional steering witnesses to verify EPR steering of polarization-entangled pairs and SS steering of single photons. The ratios between the measured witnesses and the maximum values achieved by classical mimicries are observed to increase with d for both EPR and SS steering. The designed scenario offers a new method to study further the genuine multipartite steering of large dimensionality and potential uses in quantum information processing.

Multipartite Gaussian steering: Monogamy constraints and quantum cryptography applications

We derive laws for the distribution of quantum steering among different parties in multipartite Gaussian states under Gaussian measurements. We prove that a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality holds quantitatively for a recently introduced measure of Gaussian steering. We then define the residual Gaussian steering, stemming from the monogamy inequality, as an indicator of collective steering-type correlations. For pure three-mode Gaussian states, the residual acts a quantifier of genuine multipartite steering, and is interpreted operationally in terms of the guaranteed key rate in the task of secure quantum secret sharing. Optimal resource states for the latter protocol are identified, and their possible experimental implementation discussed. Our results pin down the role of multipartite steering for quantum communication.