New Method to Reveal the Conflict Between Local Realism and Quantum Mechanics

We formulate the expectation value of the Bell-Zukowski operator acting on qubit states of a two-particle Bell experiment. By using the equivalence between a set of N copies of a two-qubit experiment and a standard two-setting Bell experiment in an entangled 2N-particle state, we obtain an inequality, which we may call the Bell-Zukowski inequality. It determines whether the measured correlation functions of two-particle states can be modeled locally and realistically. In this Bell experiment of two particles, the conflict between local realism and quantum mechanics is discussed in conjunction with the violation of the Bell-Zukowski inequality. The main point of the result is that the Bell-Zukowski operator can be represented by the Bell-Mermin operator. The threshold visibility of two-particle interference analyzed in this scheme shows good agreement with the value to cause a violation of the Bell-Zukowski inequality.Comment: To appear in Journal of the Korean Physical Society. We have introduced an additional assumption that the detector efficiency is perfect (i.e., 100%). We thank Professor Douglas G. Danforth for valuable comment

The Conflict between Bell-Zukowski Inequality and Bell-Mermin Inequality

We consider a two-particle/two-setting Bell experiment to visualize the conflict between Bell-\.Zukowski inequality and Bell-Mermin inequality. The experiment is reproducible by local realistic theories which are not rotationally invariant. We found that the average value of the Bell-\.Zukowski operator can be evaluated only by the two-particle/two-setting Bell experiment in question. The Bell-\.Zukowski inequality reveals that the constructed local realistic models for the experiment are not rotationally invariant. That is, the two-particle Bell experiment in question reveals the conflict between Bell-\.Zukowski inequality and Bell-Mermin inequality. Our analysis has found the threshold visibility for the two-particle interference to reveal the conflict noted above. It is found that the threshold visibility agrees with the value to obtain a violation of the Bell-\.Zukowski inequality.Comment: To appear in Modern Physics Letters

Unitary transformations for testing Bell inequalities

It is shown that optical experimental tests of Bell inequality violations can be described by SU(1,1) transformations of the vacuum state, followed by photon coincidence detections. The set of all possible tests are described by various SU(1,1) subgroups of Sp(8,$\Bbb R$). In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post--selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.Comment: 3 figure

Bell correlations in a many-body system with finite statistics

A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this paper, we address here the question of the statistics required to witness Bell correlated states, i.e. states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one- and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell-correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell-correlated.Comment: 5+12 pages, 3+4 figure

A Tradition of Bells: Glatfelter Bell and Hall

Every hour, students and staff hear the tolling of a bell. Some students hear it and count the number of times it rings to see what time it is. Others hear it and realize they are late to class. And many come back after they have graduated and are happy to hear the bell toll once more. There are many times when the bell is rung today. The bell is rung at graduation, funerals in the Chapel, and alumni and donor recognition. The Glatfelter Bell has been part of the Gettysburg experience since 1892. This bell is housed in one of the most iconic buildings on campus—Glatfelter Hall. The hall was built between 1887-1889, before the college considered buying the bell. Both Glatfelter and its bell have a long history that began with the building initiative of the late 1800’s beginning under the presidency of Dr. Milton Valentine and that came to fruition during the presidency of Harvey McKnight