The relativistic causality versus no-signaling paradigm for multi-party correlations.
ABSTRACT: The ubiquitous no-signaling constraints state that the probability distributions of outputs of any subset of parties in a Bell experiment are independent of remaining parties' inputs. These constraints are considered to form ultimate limits for physical correlations and led to the fields of post-quantum cryptography, randomness generation besides identifying information-theoretic principles underlying quantum theory. Here we show that while these constraints are sufficient, they are not necessary to enforce relativistic causality in multi-party correlations, i.e., the rule that correlations do not allow casual loops. Depending on the space-time coordinates of the measurement events, causality only imposes a subset of no-signaling conditions. We first consider the n-party Bell experiment (n?>?2) and identify all configurations where subsets of the constraints suffice. Secondly, we examine the implications for device-independent cryptography against an eavesdropper constrained only by relativity, detailing among other effects explicit attacks on well-known randomness amplification and key distribution protocols.
Project description:The possibility of Bell inequality violations in quantum theory had a profound impact on our understanding of the correlations that can be shared by distant parties. Generalizing the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is, however, challenging. Here, we investigate constraints on correlations in networks under the natural assumptions of no-signaling and independence of the sources. We consider the triangle network with binary outputs, and derive strong constraints on correlations even though the parties receive no input, i.e., each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network with binary outputs.
Project description:Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell's local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect.
Project description:Quantum discord is the minimal bipartite resource which is needed for a secure quantum key distribution, being a cryptographic primitive equivalent to non-orthogonality. Its role becomes crucial in device-dependent quantum cryptography, where the presence of preparation and detection noise (inaccessible to all parties) may be so strong to prevent the distribution and distillation of entanglement. The necessity of entanglement is re-affirmed in the stronger scenario of device-independent quantum cryptography, where all sources of noise are ascribed to the eavesdropper.
Project description:The key feature in correlations established by multi-party quantum entangled states is nonlocality. A quantity to measure the average nonlocality, distinguishing it from shared randomness and in a direct relation with no-signaling stochastic processes (which provide an operational interpretation of quantum correlations, without involving information transmission between the parties as to sustain causality), is proposed and resolved exhaustively for the quantum correlations established by a Clauser-Horne-Shimony-Holt setup (or CHSH box). The amount of nonlocality that is available in a CHSH box is measured by its proximity to the nearest Popescu-Rohrlich set of causal stochastic processes (aka a PR box) in the no-signaling polytope, related by polyhedral duality to Bell's correlation function. The proposed amount of average nonlocality is an entanglement monotone with a simple relation to concurrence. We provide the optimal setup vectors of a maximally nonlocal CHSH box for any entangled pair. The strongest nonlocality is the fraction [Formula: see text] of a PR box, attained by maximally entangled qubit pairs. The most economical causal stochastic process reproducing any maximally nonlocal CHSH box is developed. Data produced by a computer implementation of the simulator agrees with the quantum mechanical formulas.
Project description:Quantum mechanics admits correlations that cannot be explained by local realistic models. The most studied models are the standard local hidden variable models, which satisfy the well-known Bell inequalities. To date, most works have focused on bipartite entangled systems. We consider correlations between three parties connected via two independent entangled states. We investigate the new type of so-called "bilocal" models, which correspondingly involve two independent hidden variables. These models describe scenarios that naturally arise in quantum networks, where several independent entanglement sources are used. Using photonic qubits, we build such a linear three-node quantum network and demonstrate nonbilocal correlations by violating a Bell-like inequality tailored for bilocal models. Furthermore, we show that the demonstration of nonbilocality is more noise-tolerant than that of standard Bell nonlocality in our three-party quantum network.
Project description:We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.
Project description:Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.
Project description:Device-independent cryptography goes beyond conventional quantum cryptography by providing security that holds independently of the quality of the underlying physical devices. Device-independent protocols are based on the quantum phenomena of non-locality and the violation of Bell inequalities. This high level of security could so far only be established under conditions which are not achievable experimentally. Here we present a property of entropy, termed "entropy accumulation", which asserts that the total amount of entropy of a large system is the sum of its parts. We use this property to prove the security of cryptographic protocols, including device-independent quantum key distribution, while achieving essentially optimal parameters. Recent experimental progress, which enabled loophole-free Bell tests, suggests that the achieved parameters are technologically accessible. Our work hence provides the theoretical groundwork for experimental demonstrations of device-independent cryptography.
Project description:Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles.
Project description:Multipartite entangled states are a fundamental resource for a wide range of quantum information processing tasks. In particular, in quantum networks, it is essential for the parties involved to be able to verify if entanglement is present before they carry out a given distributed task. Here we design and experimentally demonstrate a protocol that allows any party in a network to check if a source is distributing a genuinely multipartite entangled state, even in the presence of untrusted parties. The protocol remains secure against dishonest behaviour of the source and other parties, including the use of system imperfections to their advantage. We demonstrate the verification protocol in a three- and four-party setting using polarization-entangled photons, highlighting its potential for realistic photonic quantum communication and networking applications.