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In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in…

We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private…

Quantum Physics · Physics 2023-04-05 Cameron Foreman , Sherilyn Wright , Alec Edgington , Mario Berta , Florian J. Curchod

We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…

Rings and Algebras · Mathematics 2019-07-31 Nam van Tran , Imme van den Berg

Non-local correlations are usually understood through the outcomes of alternative measurements (on two or more parts of a system) that cannot altogether actually be carried out in an experiment. Indeed, a joint input/output -- e.g.,…

Quantum Physics · Physics 2015-11-11 Stefan Wolf

Self-testing is a device-independent examination of quantum devices based on correlations of observed statistics. Motivated by elegant progresses on self-testing strategies for measurements [Phys. Rev. Lett. 121, 250507 (2018)] and for…

Quantum Physics · Physics 2021-12-28 Qing Zhou , Xin-Yu Xu , Shuai Zhao , Yi-Zheng Zhen , Li Li , Nai-Le Liu , Kai Chen

Hypothesis testing plays a central role in statistical inference, and is used in many settings where privacy concerns are paramount. This work answers a basic question about privately testing simple hypotheses: given two distributions $P$…

Data Structures and Algorithms · Computer Science 2019-04-04 Clément L. Canonne , Gautam Kamath , Audra McMillan , Adam Smith , Jonathan Ullman

There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general…

Quantum Physics · Physics 2024-02-09 Jaskaran Singh , Adán Cabello

Physical theories constrained with local quantum structure and satisfying the no-signalling principle can allow beyond-quantum global states. In a standard Bell experiment, correlations obtained from any such beyond-quantum bipartite state…

One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…

Quantum Physics · Physics 2013-11-14 Somshubhro Bandyopadhyay , Michael Nathanson

While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through…

In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell…

Quantum Physics · Physics 2020-01-22 Anna de Rosier , Jacek Gruca , Fernando Parisio , Tamas Vertesi , Wieslaw Laskowski

Self-testing refers to the fact that, in some quantum devices, both states and measurements can be assessed in a black-box scenario, on the sole basis of the observed statistics, i.e. without reference to any prior device calibration. Only…

Some aspects of the development of physics and the mathematics set one think about relation between complex numbers and reality around us. If number to spot as the relation of two quantities, from the fact of existence of complex numbers…

General Physics · Physics 2007-05-23 V. V. Lyahov , V. M. Nechshadim

We study a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state $\Phi^+$ and (2) two commuting but otherwise unknown measurement apparatus, one on each side, that…

Quantum Physics · Physics 2007-05-23 Dominic Mayers , Andrew Yao

We introduce a systematic approach for analyzing device-independent single-prover interactive protocols under computational assumptions. This is done by establishing an explicit correspondence with Bell inequalities and nonlocal games and…

Quantum Physics · Physics 2025-10-13 Ilya Merkulov , Rotem Arnon

We describe a simple method to derive high performance semidefinite programming relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program and…

Quantum Physics · Physics 2015-07-15 Miguel Navascues , Tamas Vertesi

We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…

Algebraic Geometry · Mathematics 2008-06-27 Adel Khalfallah , Siegmund Kosarew

Quantum networks of growing complexity play a key role as resources for quantum computation; the ability to identify the quality of their internal correlations will play a crucial role in addressing the buiding stage of such states. We…

In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…

Computational Complexity · Computer Science 2018-05-08 Masaki Nakanishi , Marcos Villagra

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Statistics Theory · Mathematics 2022-02-17 Jack Noonan , Anatoly Zhigljavsky