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We study the problem of fair binary classification using the notion of Equal Opportunity. It requires the true positive rate to distribute equally across the sensitive groups. Within this setting we show that the fair optimal classifier is…

Statistics Theory · Mathematics 2020-02-05 Evgenii Chzhen , Christophe Denis , Mohamed Hebiri , Luca Oneto , Massimiliano Pontil

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…

Quantum Physics · Physics 2022-04-12 G. S. Ciepielewski , E. Okon

In an empirical logic, an experimentally verifiable proposition P relating to a quantum system is assigned the value of either true of false if the system is in the pure state that belongs or, respectively, does not belong to the Hilbert…

Quantum Physics · Physics 2019-05-01 Arkady Bolotin

Statistical tests are needed to determine experimentally whether a hypothetical theory based on local realism can be an acceptable alternative to quantum mechanics. It is impossible to rule out local realism by a single test, as often…

Quantum Physics · Physics 2017-04-26 Asher Peres

Viewing two astronomical sources at large enough distance and angular separation can assure, by light-travel-time arguments, the acausality of their emitted photons. Using such photons to set apparatus parameters in a laboratory-based…

Cosmology and Nongalactic Astrophysics · Physics 2020-06-30 Eric Steinbring

We construct a hidden variable model for the EPR correlations using a Restricted Boltzmann Machine. The model reproduces the expected correlations and thus violates the Bell inequality, as required by Bell's theorem. Unlike most…

Quantum Physics · Physics 2017-07-19 Steven Weinstein

On one side, so far a great part of the evidence accepted as proof of the alleged quantum non-locality relied on inhomogeneous Bell inequalities involving an additional assumption (no-enhancement) whose role had not been sufficiently…

Mathematical Physics · Physics 2015-03-19 David Rodríguez

An experiment is proposed to test Bell's theorem in a purely macroscopic domain. If realized, it would determine whether Bell inequalities are satisfied for a manifestly local, classical system. It is stressed why the inequalities should…

Quantum Physics · Physics 2009-06-29 Joy Christian

A nonclassical feature of the fourth-order interference at a beam splitter, that genuine photon spin singlets are emitted in predetermined directions even when incident photons are unpolarized, has been used in a proposal for an experiment…

Quantum Physics · Physics 2009-10-31 Mladen Pavicic

We show theoretically that Bell-type correlations can be observed between continuous variable measurements performed on a parametric source. An auxiliary measurement, performed on the detection environment, negates the possibility of…

Quantum Physics · Physics 2009-11-06 T. C. Ralph , W. J. Munro , R. E. S. Polkinghorne

We discuss coupling of violation of Bell's inequality and non-Kolmogorovness of statistical data in the EPR-Bohm experiment. We emphasize that nonlocalty and "death of realism" are only sufficient, but not necessary conditions of…

Quantum Physics · Physics 2012-10-09 Andrei Khrennikov

We present the experimental results of measurements of the overlap of both pure and mixed polarization states of photons. The fidelity and purity of mixed states were also measured. The experimental apparatus exploits the fact that a beam…

Quantum Physics · Physics 2009-11-07 Martin Hendrych , Miloslav Dusek , Radim Filip , Jaromir Fiurasek

In the well-studied (2,2,2) Bell experiment consisting of two parties, two measurement settings per party, and two possible outcomes per setting, it is known that if the experiment obeys no-signaling constraints, then the set of admissible…

Quantum Physics · Physics 2016-04-26 Peter Bierhorst

Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…

Quantum Physics · Physics 2018-04-19 R. Rossi , Leonardo A. M. Souza

We describe an experiment in which two non communicating computers, starting from a common input in the form of sequences of pseudo--random numbers in the interval $[0,2\pi]$, and computing deterministic $\{\pm 1\}$--valued functions,…

Quantum Physics · Physics 2007-05-23 Luigi Accardi , Massimo Regoli

In Bell experiments, one problem is to achieve high enough photodetection to ensure that there is no possibility of describing the results via a local hidden-variable model. Using the Clauser-Horne inequality and a two-photon non-maximally…

Quantum Physics · Physics 2022-03-16 Adan Cabello , Jan-Åke Larsson

A local, time-retarded hidden variable model is described that fits the recently measured EPR data from the Innsbruck collaboration. The model is based on the idea that waves in the zero-point field convey information from the detectors to…

Quantum Physics · Physics 2007-05-23 Michael Clover

We show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially-separated parties who perform local measurements on a…

Quantum Physics · Physics 2016-09-08 Yeong-Cherng Liang , Nicholas Harrigan , Stephen D. Bartlett , Terry Rudolph

Fabricating experimental pictures in research work is a serious academic misconduct, which should better be detected in the reviewing process. However, due to large number of submissions, the detection whether a picture is fabricated or…

Computer Vision and Pattern Recognition · Computer Science 2020-02-11 Binrui Shen , Qiang Niu , Shengxin Zhu

Quantum theory is inconsistent with any local hidden variable model as was first shown by Bell. To test Bell inequalities two separated observers extract correlations from a common ensemble of identical systems. Since quantum theory does…

Quantum Physics · Physics 2011-01-19 Shmuel Marcovitch , Benni Reznik