Non-local boxes are hypothetical ``machines'' that give rise to superstrong non-local correlations, leading to a stronger violation of Bell/CHSH inequalities than is possible within the framework of quantum mechanics. We show how non-local boxes can be used to perform any two-party secure computation. We first construct a protocol for bit commitment and then show how to achieve oblivious transfer using non-local boxes. Both have been shown to be impossible using quantum mechanics alone.
This Letter looks at the consequences of so-called 'superstrong nonlocal correlations', which are hypothetical violations of Bell/CHSH inequalities that are stronger than quantum mechanics allows, yet weak enough to prohibit faster-than-light communication. It is shown that the existence of maximally superstrong correlated bits implies that all distributed computations can be performed with a trivial amount of communication, i.e. with one bit. If one believes that Nature does not allow such a computational 'free lunch', then the result in the Letter gives a reason why superstrong correlation a…
Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography protocols. It is known that networks beyond that in the paradigmatic Bell's theorem imply new and sometimes stronger forms of nonclassicality. Due to a number of practical difficulties, however, the experimental implementation of such networks remains far less explored. Going beyond what has been previously tested, here we verify the nonlocality of an experimental tr…
Energy-time entangled biphoton source plays a great role in quantum communication, quantum metrology and quantum cryptography due to its strong temporal correlation and capability of nonlocal dispersion cancellation. As a quantum effect, nonlocal dispersion cancellation is further proposed as an alternative way for nonlocality test of continuous variable entanglement via the violation of Bell-like inequality proposed by Wasak et al. [Phys. Rev. A, 82, 052120 (2010)]. However, to date there is no experimental report either on the inequality violation or on a nonlocal detection with single-photo…
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…
Information sources used for communication purposes usually are assumed to be i.i.d. type, especially as far as entanglement or nonlocality properties are concerned. Here we proposed simple scheme for detection of nonlocality of non i.i.d. sources based on the program idea which can be useful in communication tasks including quantum cryptography and communication complexity reduction. The principle of the scheme is rather general and can be applied to other problems like detection of entanglement coming from non-i.i.d sources.
Quantum steering, loosely speaking the distribution of entanglement from an untrusted party, is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. Determining which states can be steered is important from a conceptual point of view, but also for applications, e.g. in quantum cryptography. Here we show that bound entanglement, although it represents the weakest form of entanglement, can nevertheless lead to quantum steering. This is done by noticing that steering inequalities can be derived from entropic uncertainty relations. Our result has implicati…
These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how physics could be even more general than quantum, I present two conceivable phenomena beyond QT: superstrong nonlocality and higher-order interference. Then I introduce the framework of GPTs, generalizing both quantum and classical probability theory. Finally, I summarize a reconstruction of QT from the principles of Tomographic Locality, Continuous Reversibility,…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and besides its impact on our view of the world, it can be exploited for applications such as quantum cryptography and quantum computing. (...) Although entanglement and nonlocality are ordinarily regarded as one and the same, under close consideration this cannot be taken for granted. The reason for this is that entanglement is defined by the mathematical structure…
Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here, we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidde…
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classica…
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such that their outcomes cannot both be predicted. On the other hand, nonlocal correlations of measurement outcomes at different locations cannot be explained by classical physics, but appear in the presence of entanglement. Here, we show that these two fundamental quantum effects are quantitatively related. Namely, we provide an entropic uncertainty relation for …
Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which is defined in the simplest scenario involving two dichotomic measurements and whose all key properties are well understood. There have been many attempts to generalise the CHSH Bell inequality to higher-dimensional quantum systems, however, for most of them the maximal quantum violation---the key quantity for mos…
Probing many-body Bell correlation depth with superconducting qubits
School of Physics, Zhejiang University（浙江大学物理学院）；Center for Quantum Information, IIIS, Tsinghua University（清华大学信息科学技术研究院量子信息中心）；Instituut-Lorentz, Universiteit Leiden（莱顿大学洛伦兹研究所）；ZJU-Hangzhou Global Scientific and Technological Innovation Center（浙江大学杭州国际科技创新中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Qi Zhi Institute（上海量子科学研究中心）
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such as superposition, entanglement, and nonlocality --- poses deep puzzles about the underlying physical reality, even while these same features are at the heart of exciting developments such as quantum cryptography, algorithms, and computing. These puzzles might be resolved if the mathematical structure of quantum mechanics were built up from physically interpre…
