Abstract The swapping of various quantum correlation measures is addressed including, Bell‐nonlocality, Einstein–Podolsky–Rosen steering, usefulness for teleportation, and entanglement, as well as quantum obesity as a quantum correlation more general than entanglement. The effects that local filtering operations have on the swapping of such correlations are particularly focused. Based on a generalization of entanglement swapping with arbitrary two‐qubit states and arbitrary measurements, analytical formulae for the swapping of two‐qudit as well as multi‐qubit quantum states are derived and the exact amount of quantum obesity that is swapped is provided. Then, in order to enhance the final amount of correlations in the post‐swapping two‐qubit state, the action of local filters before as well as after the swapping protocol is explored. In this regard, it is conjectured that applying local filters first is more efficient. This is supported by an analytical proof on the quantum obesity of almost Bell‐diagonal states, as well as numerical evidence for all the considered quantum correlations of arbitrary X‐form states.
Abstract The swapping of various quantum correlation measures is addressed including, Bell‐nonlocality, Einstein–Podolsky–Rosen steering, usefulness for teleportation, and entanglement, as well as quantum obesity as a quantum correlation more general than entanglement. The effects that local filtering operations have on the swapping of such correlations are particularly focused. Based on a generalization of entanglement swapping with arbitrary two‐qubit states and arbitrary measurements, analytical formulae for the swapping of two‐qudit as well as multi‐qubit quantum states are derived and the exact amount of quantum obesity that is swapped is provided. Then, in order to enhance the final amount of correlations in the post‐swapping two‐qubit state, the action of local filters before as well as after the swapping protocol is explored. In this regard, it is conjectured that applying local filters first is more efficient. This is supported by an analytical proof on the quantum obesity of almost Bell‐diagonal states, as well as numerical evidence for all the considered quantum correlations of arbitrary X‐form states.
Einstein-Podolsky-Rosen (EPR) steering, a fundamental concept of quantum nonlocality, describes one observer's capability to remotely affect another distant observer's state by local measurements. Unlike quantum entanglement and Bell nonlocality, both associated with the symmetric quantum correlation, EPR steering depicts the unique asymmetric property of quantum nonlocality. With the local filter operation in which some system components are discarded, quantum nonlocality can be distilled to enhance the nonlocal correlation and even the hidden nonlocality can be activated. However, asymmetric quantum nonlocality in the filter operation still lacks a well-rounded investigation, especially considering the discarded parts where quantum nonlocal correlations may still exist with probabilities. Here, in both theory and experiment, we investigate the effect of reusing the discarded particles from local filter. We observe all configurations of EPR steering simultaneously and other intriguing evolution of asymmetric quantum nonlocality, such as reversing the direction of one-way EPR steering. This work provides a perspective to answer ``what is the essential role of utilizing quantum steering as a resource?'' and demonstrates a practical toolbox for manipulating asymmetric quantum systems with significant potential applications in quantum information tasks.
We study how different types of quantum correlations can be established as the consequence of a generalized entanglement swapping protocol where, starting from two Bell pairs (1,2) and (3,4), a general quantum measurement [denoted by a positive operator-valued measure (POVM)] is performed on the pair (2,3), which results in creating quantum correlation in (1,4) shared between two spatially separated observers. Contingent upon using different kinds of POVMs, we show generation or destruction of different quantum correlations in the pairs (1,4), (1,2), and (3,4). This thus reflects nontrivial transfer of quantum correlations from the pairs (1,2) and (3,4) to the pair (1,4). As an offshoot, this paper provides an operational tool to generate different types of single parameter families of quantum correlated states [for example, entangled but not Einstein-Podolsky-Rosen (EPR) steerable, or EPR steerable but not Bell nonlocal, or Bell nonlocal] by choosing different quantum measurements in the basic entanglement swapping setup. We further extend our paper by taking mixed initial states shared by the pairs (1,2) and (3,4). Finally, we study network nonlocality in our scenario. Here, we find the appropriate POVM measurement for which the generated correlation demonstrates or does not demonstrate network nonlocality for the whole range of the measurement parameter.
The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.
We prove, modulo a conjecture on quantum steering ellipsoids being true, the existence of the phenomenon of locally inaccessible hidden quantum correlations, that is, the existence of two-particle states whose hidden quantum correlations cannot be revealed by local filters implemented exclusively on one side of the experiment but that can still be revealed when both parties cooperate in applying judiciously chosen local filters. The quantum correlations considered here are the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell nonlocality and the violation of the F3 inequality for Einstein-Podolsky-Rosen steering. Specifically, we provide a necessary criterion for guaranteeing the presence of such phenomena for arbitrary two-qubit states. This criterion in turn relies on the conjecture that the maximal violations of CHSH inequality and F3 inequality are both upper bounded by functions that depend on the magnitude of the quantum steering ellipsoid center. This latter conjecture, although currently lacking an analytical proof, is supported by numerical results. We use this necessary criterion to explicitly show examples of two-qubit states with locally inaccessible hidden quantum correlations and furthermore two-qubit states with locally inaccessible maximal hidden quantum correlations.
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.
The nonlocal correlations between quantum states in an entangled system are essential to many quantum communications applications. A basic quantum operation, which permits the distribution of entanglement between two initially uncorrelated systems, is entanglement swapping. Here we present a rigorous formulation of entanglement swapping of any two partially mixed two-qubit states without limiting ourselves to any specific type of state or noise. Further, for two important classes of the input states, Bell diagonal and pure states, we describe how the concurrence of the final state is related to the concurrence of the initial states. First, we consider Bell diagonal states, and find bounds on the concurrence of the final state in terms of the concurrences of the initial states. These bounds are important for communications applications because polarization mode dispersion in fibers produces Bell diagonal states up to a local unitary rotation. Second, we show that swapping pure states occasionally results in a state of higher concurrence than either of the initial states. In addition, we find that two pure states are most likely to be capable of swapping to a state of increased concurrence when the two initial states have similar concurrences. Our analysis offers a completely general framework for investigating the behavior of any pair of two-qubit states when used for entanglement swapping.