We first present a protocol for deterministically distilling non-locality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of post-quantum non-local boxes, which we term correlated non-local boxes. In the asymptotic limit, all correlated non-local boxes are distilled to the maximally non-local box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard \textit{et al.} [Phys. Rev. Lett. 96, 250401 (2006)] we show that all correlated non-local boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these non-local boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum non-locality is limited.
In quantum mechanics some spatially separated sub-systems behave as if they are part of a single system, the superposition of states of this single system cannot be written as products of states of individual sub-systems,we say that the state of such system is entangled, such systems give rise to non-local correlations between outcomes of measurements. The non-local correlations are conditional probability distributions of some measurement outcomes given some measurement settings and cannot be explained by shared information.These correlations can be studied using a non-local box(NLB) which ca…
In [Phys. Rev. Lett. 114, 250401 (2015)] the sharing of non-locality by multiple observers was demonstrated through the quantum violation of Clauser-Horne-Shimony-Halt inequality. In this paper we provide a scheme for sharing of non-locality and non-trivial preparation contextuality sequentially through the quantum violation of a family of Bell's inequalities where Alice and Bob perform $2^{n-1}$ and $n$ numbers of measurements of dichotomic observables respectively. For this, we consider that Alice always performs projective measurement and multiple Bobs sequentially perform unsharp measureme…
A unified view on the phenomenon of monogamy exhibited by Bell inequalities and non-contextuality inequalities arising from the no-signaling and no-disturbance principles is presented using the graph-theoretic method introduced in \textit{Phys. Rev. Lett. 109, 050404 (2012)}. We propose a novel type of trade-off, namely Bell inequalities that do not exhibit monogamy features of their own can be activated to be monogamous by the addition of a local contextuality term. This is illustrated by means of the well-known $\mathcal{I}_{3322}$ inequality, and reveals a resource trade-off between biparti…
Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable operations. Moreover, these constraints combine non-trivially with the potential requirement that operations be performed locally. The combination of symmetry and locality constraints influence our ability to perform quantum error correction in two counterposing ways. On the one hand, they constrain the effect of noise, limiting its possible action over the quantum …
We give a set of necessary conditions for locality in bipartite systems, which include and generalize known Bell's inequalities. Each condition corresponds to a specific order of the expansion of random variables defined on graphs, in terms of genuinely n-variable correlation functions. The first non-trivial order leads to known Bell inequalities, while higher orders produce additional, non-equivalent conditions. In particular, in CHSH settings, we obtain at least two additional tight conditions which do not reduce to the CHSH inequality. This shows that tight Bell inequalities are sufficient …
Measuring Bell non-locality in the presence of signaling
City St George’s, University of London（伦敦大学城市圣乔治学院）；Technische Hochschule Mittelhessen（黑森中部应用技术大学）；Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）
Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that $1$D and $2$D quantum voids --faces of the nonlocal simplex set with no quantum realization-- can be…
Standard multiparty Bell experiments involve a single source shared by a set of observers. In contrast, network Bell experiments feature multiple independent sources, and each of them may distribute physical systems to a set of observers who perform randomly chosen measurements. The $n$-locality scenario in star-network configuration involves $n$ number of edge observers (Alices), a central observer (Bob), and $n$ number of independent sources having no prior correlation. Each Alice shares an independent state with the central observer Bob. Usually, in network Bell experiments, one considers t…
While initial versions of Bell's theorem captured the notion of locality with the assumption of factorizability, in later presentations, Bell argued that factorizability could be derived from the more fundamental principle of local causality. Here we show that, contrary to what is commonly assumed, in order to derive factorizability from the principle of local causality, a non-trivial assumption, similar but strictly independent of settings independence, is required. Loosely speaking, such an extra assumption demands independence between the states of the measurement apparatuses. We conclude t…
We introduce a new feature of no-signaling (Bell) non-local theories, namely, when a system of multiple parties manifests genuine non-local correlation, then there cannot be arbitrarily high non-local correlation among any subset of the parties. We call this feature, \textit{complementarity of genuine multipartite non-locality}. We use Svetlichny's criterion for genuine multipartite non-locality and non-local games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compar…
Nonlocal correlations are a central feature of quantum theory, and understanding why quantum theory has a limited amount of nonlocality is a fundamental problem. Since nonlocality also has technological applications, e.g., for device-independent cryptography, it is useful to understand it as a resource and, in particular, whether and how different types of nonlocality can be interconverted. Here we focus on nonlocality distillation which involves using several copies of a nonlocal resource to generate one with more nonlocality. We introduce several distillation schemes which distil an extended…
Bell non-locality represents one of the most striking departures of quantum mechanics from classical physics. It shows that correlations between space-like separated systems allowed by quantum mechanics are stronger than those present in any classical theory. In a recent work [Sci. Adv. 7, eabc3847 (2021)], a family of Bell functionals tailored to mutually unbiased bases (MUBs) is proposed. For these functionals, the maximal quantum violation is achieved if the two measurements performed by one of the parties are constructed out of MUBs of a fixed dimension. Here, we generalize this constructi…
We present a security proof for establishing private entanglement by means of recurrence-type entanglement distillation protocols over noisy quantum channels. We consider protocols where the local devices are imperfect, and show that nonetheless a confidential quantum channel can be established, and used to e.g. perform distributed quantum computation in a secure manner. While our results are not fully device independent (which we argue to be unachievable in settings with quantum outputs), our proof holds for arbitrary channel noise and noisy local operations, and even in the case where the ea…
We study symmetry-protected topological (SPT) phases of matter in 2D protected by symmetries acting on fractal subsystems of a certain type. Despite the total symmetry group of such systems being subextensively large, we show that only a small number of phases are actually realizable by local Hamiltonians. Which phases are possible depends crucially on the spatial structure of the symmetries, and we show that in many cases no non-trivial SPT phases are possible at all. In cases where non-trivial SPT phases do exist, we give an exhaustive enumeration of them in terms of their locality.
We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints. Our central result is a linear-algebraic necessary and sufficient condition for a generic (full-rank) target state to be frustration-free quasi-locally stabilizable, along with an explicit procedure for constructing Markovian dynamics that achieve stabilization. If the target state is not full-rank, we establish sufficiency under an additional condition, whic…
Geometrically nontrivial quantum states can be defined as states that cannot be prepared by a constant depth geometrically local unitary circuit starting from a product state. However, for topological phases, as well as a large class of quantum error correcting codes without an underlying geometric structure, the required circuit depth remains infinite even if we replace the condition of geometric locality with the weaker condition of k-locality. Motivated by this observation, we look for a non-geometric quantity that can capture k-local non-triviality of a given state, for example, we ask if …
Non-locality is the phenomenon of observing strong correlations among the outcomes of local measurements of a multipartite physical system. No-signaling boxes are the abstract objects for studying non-locality, and wirings are local operations on the space of no-signaling boxes. This means that, no matter how non-local the nature is, the set of physical non-local correlations must be closed under wirings. Then, one approach to identify the non-locality of nature is to characterize closed sets of non-local correlations. Although non-trivial examples of wirings of no-signaling boxes are known, t…
We study locality preserving automorphisms of operator algebras on $D$-dimensional uniform lattices of prime $p$-dimensional qudits (QCA), specializing in those that are translation invariant (TI) and map every prime $p$-dimensional Pauli matrix to a tensor product of Pauli matrices (Clifford). We associate antihermitian forms of unit determinant over Laurent polynomial rings to TI Clifford QCA with lattice boundaries, and prove that the form determines the QCA up to Clifford circuits and shifts (trivial). It follows that every 2D TI Clifford QCA is trivial since the antihermitian form in this…
