Nonlocality of all quantum networks

Abstract

The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question: how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce a new approach to prove the generic activated nonlocality as a result of entanglement swapping for all bipartite entangled states. The result is further applied to show the multipartite nonlocality and activated nonlocality for all nontrivial quantum networks consisting of any entangled states. Our results provide the nonlocality witnesses and quantum superiorities of all connected quantum networks or nontrivial hybrid networks in contrast to classical networks. arXiv:1806.09758v1 [quant-ph] 26 Jun 2018 {τ a1 , ∀a 1 }, · · · , {τ an , ∀a n } are assumed for all observers shown in Figure 1. It follows a new joint conditional probability distribution asSimilar to verifying single entanglement [2, 8], how to decide the nonlocality of a quantum network is also a fundamental question. Nevertheless, identifying the nonlocality of a general quantum network remains an extremely difficult problem [40][41][42][43][44][45][46][47].Here, we introduce a new framework for exploring the nonlocality of all quantum networks. Given a quantum network consisting of a joint quantum system ρ = ρ 1 ⊗ · · · ⊗ ρ k shared by n observers, the main idea is to create quantum subnetworks for special observers (Alice and Charlie shown in Figure 1). If some nonlocal correlations can be observed in these subnetworks, they are provided by the quantum state ρ, which is then multipartite nonlocal. Within the new scenario, we investigate the activation phenomena for these subnetworks consisting of all independent observers without prior sharing entanglement. It is of the multipartite nonlocality in a network scenario.Definition 1. A quantum network N q is multipartite nonlocal if a set of observables existing for all observers such that multipartite quantum correlations from local measurements are inconsistent with these from the generalized local realism.Definition 2. A quantum network N q consisting of n observers is k-partite activated nonlocal if for any s observers p i1 , · · · , p is with 2 ≤ s ≤ k, there is a set of observables for all observers such that a local measurement of n − s observers p j s with j ∈ {1, · · · , n}\{i 1 , · · · , i s } creates a s-partite nonlocal subnetwork.Nonlocality of all Λ-shaped quantum networks. Consider a Λ-shaped quantum network N q consisting of three observers Alice, Bob and Charlie shown in Figure 1. The nontrivial feature of N q is entanglement swapping [26,41]. Different from the standard nonlocality [3, 6, 8, 9] de...

Quantifying algebraic asymmetry of Hamiltonian systems

“…The asymmetry has been defined and its properties have been investigated. As detailed applications, the asymmetries of the q-deformed harmonic Hamiltonian system (9) with respect to the harmonic operator representation (5) of su(2), the q-deformed Casimir operator (14) with respect to the co-product representation (15) of su(2), and the integrable spin chain Hamiltonian (21) with respect to the su(2) representation (20) have been computed an-alytically. In particular, the asymmetry (1) presents a qualitative characterization of the degree of geometrical deformation of sphere.…”

“…The quantification of the symmetry or asymmetry of a quantum system is of significance. The asymmetry of quantum states with respect to groups has been studied in the view of resource, such as coherence [15][16][17][18][19][20][21]. In [22] the cost of symmetrization of quantum states has been investigated.…”

Certification of Genuine Multipartite Entanglement with General and Robust Device-independent Witnesses

“…Furthermore, for the known inequalities the complexity (number of different measurement to perform) typically increases exponentially with the number of parties, making them impractical. To date, DIC has been intensively investigated for a few simple types of multipartite entangled states [32][33][34][35], and several specific genuinely entangled states [36][37][38][39] have been investigated. Similarly, self-testing, an approach allowing one to identify the quantum state device-independently was only pursued for a few states [40][41][42][43][44][45].…”

Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

“…Next the Bell-type inequalities for star-shaped and noncyclic networks were studied [17,18]. Recently, broader classes of quantum networks based on locally causal structures have also been investigated [19,20,23,24]. In particular, computationally efficient algorithms for constructing Bell inequalities have been proposed [20].…”