Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)
Maximisation of Quantum Correlations under Local Filtering Operations
Sabine Wollmann, Laurent Kling, Graham D. Marshall, Raffaele Santagati, Timothy C. Ralph, Jingbo B. Wang, Jeremy L. OaBrien, Mark G. Thompson, Paul Skrzypczyk, Jonathan C. F. Matthews, Andrés F. Ducuara, Xiaogang Qiang, Joel F. Tasker, Xiaoqi Zhou, Jianwei Wang, Callum M. Wilkes, T. Loke, Sean OaGara
Nonclassical correlations are a key resource to explore foundational quantum information tasks and find applications in device-independent protocols. Quantum steering was formalized in 2007 [1] and is distinct from other nonclassical correlations such as Bell nonlocality [2] and entanglement. Steering describes the effect of a local measurement on one system and affecting the measurement results on the other system. This can be visualized for two-qubit states using quantum steering ellipsoids (QSE), which is the set of Bloch vectors that Alice can collapse Bob's state to. They are theoretically well studied [3-6] and have been recently experimentally demonstrated [7].
Nonclassical correlations are a key resource to explore foundational quantum information tasks and find applications in device-independent protocols. Quantum steering was formalized in 2007 [1] and is distinct from other nonclassical correlations such as Bell nonlocality [2] and entanglement. Steering describes the effect of a local measurement on one system and affecting the measurement results on the other system. This can be visualized for two-qubit states using quantum steering ellipsoids (QSE), which is the set of Bloch vectors that Alice can collapse Bob's state to. They are theoretically well studied [3-6] and have been recently experimentally demonstrated [7].
Quantum entanglement is a key resource for foundational quantum information and communication tasks, such as teleportation, entanglement swapping and quantum key distribution [1]. Quantum steering is a quantum correlation that is distinct from other nonclassical correlations such as Bell nonlocality [2] and entanglement. Steering describes the effect of measuring one system, let's say Alice, and affecting the measurement results on the other system, let's say Bob. Moving through the hierarchy of nonlocal classes, from Bell nonlocality towards nonsepa-rability, requires an increasing number of parties and apparatus that need to be trusted but gives access to protocols which are more robust to noise for projective measurements [3,4]. In a quantum steering task [5] the correlations of Alice and Bob's measurement outcomes are tested against a classical probability bound which can be only violated if the state shared between the parties is quantum steerable.
Quantum steering ellipsoids (QSEs) provide a geometric representation, within the Bloch picture, of all possible states to which one qubit can be steered through measuring another correlated qubit. However, in realistic settings, quantum systems are inevitably coupled to their environment, resulting in decoherence and degradation of the QSE. Here, by investigating how local dissipative environments coupled to each qubit affect the quantum steering, we find that the geometry of each party's QSE is closely tied to the non-Markovian effect and the formation of a bound state in the energy spectrum of the total qubit-environment system. The bound state provides the ability and the non-Markovian effect provides the dynamical way for preserving the QSE. We systematically examine the characteristics of QSEs under three distinct scenarios, i.e., two-sided bound states, one-sided bound states, and no bound state, revealing a diverse range of steering types. Our work establishes quantum reservoir engineering as a tunable strategy for protecting and controlling quantum steering in open systems, offering a practical pathway toward robust steering-based quantum technologies.
Abstract 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.
Abstract Nonclassicality is seen as an important physical resource and offers quantum advantages in modern quantum information processing. Motivated by recent work on the interplay between Bell nonlocality and nonclassicality quantified by average correlation [ Phys. Rev. Res. 5 023063 (2023)], in this paper we aim to establish the intrinsic relationship between the average correlation and the violation of the three-setting linear steering inequality for arbitrary two-qubit states. The results suggest that average correlation is closely related to the violation of the three-setting linear steering inequality, like its relationship with Bell inequality violation. Moreover, the dynamical behaviors of average correlation and steering are carefully analyzed under the influence of local unital and nonunital noisy channels. Particularly, for any two-qubit states, the hierarchy of average correlation-steering-Bell nonlocality is demonstrated by using the singular value decomposition theorem.
It is well known that quantum correlations such as quantum nonlocality and steering can be revealed by means of the implementation of local filters or stochastic local operation and classical communication (SLOCC). This means that bipartite quantum states that are entangled but local (unsteerable), can be driven locally to quantum nonlocal (steerable) states. However, there does not exist a criterion telling us whether the revealed quantum correlation is accessible by locally implementing on a single party, or both parties are required to cooperate by implementing local filters. In this work, we proposed a criterion based on the quantum steering ellipsoid and provided examples of two-qubit states with locally inaccessible quantum correlations.
Quantum nonlocality and nonclassicality are two remarkable characteristics of quantum theory, and offer quantum advantages in some quantum information processing. Motivated by recent work on the interplay between nonclassicality quantified by average correlation [Tschaffon et al., Phys. Rev. Res. 5,023063 (2023)] and Bell nonlocality, in this paper we aim to establish the relationship between the average correlation and the violation of the three-setting linear steering inequality for two-qubit systems. Exact lower and upper bounds of average correlation versus steering are obtained, and the respective states which suffice those bounds are also characterized. For clarity of our presentation, we illustrate these results with examples from well-known classes of two-qubit states. Moreover, the dynamical behavior of these two quantifiers is carefully analyzed under the influence of local unital and nonunital noisy channels. The results suggest that average correlation is closely related to the violation of three-setting linear steering, like its relationship with Bell violation. Particularly, for a given class of states, the hierarchy of nonclassicality-steering-Bell nonlocality is demonstrated.