Some Puzzles and Unresolved Issues About Quantum Entanglement

Jozef Gruska, Hiroshe Imai, Hiroshi Imai

F.J. Duarte

C. S. Unnikrishnan

The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.

Chetan Waghela

Balance (Counterfeit coin) puzzles have been part of recreational mathematics for a few decades. A particular type of Counterfeit coin puzzle is known in the literature as the "Beam balance puzzle". An abstract solution to it is provided by Iwama et.al as a modification of the Bernstein-Vazirani algorithm, making use of quantum parallelism and entanglement. Moreover, during this pandemic, group testing has proved to be an efficient algorithm to save time and cost of testing specimens for the presence of infection. In this article, we propose a "Binary Spring Balance" (BSB) puzzle, to facilitate a unified picture of the counterfeit coin problem and the testing for infection problem, as both aim to reduce the number of queries. We then showcase two solutions to the BSB problem, one using bits and other using classical-qubits ('cebits") for querying. Both solutions are demonstrated using circuits. In this pursuit, we develop a modified optical implementation of Bernstein-Vazirani algorithm using only polarizers (no need of beam splitters), which has surprisingly not yet been proposed earlier. Under the pretext of this demonstration we question why we have not yet developed testing mechanisms inspired by Bernstein-Vazirani algorithm for the pandemic, as they solve the problem in single query, they have no issues related to prevalence of infection in the population, nor are they plagued by the issue of dilution of samples due to pooling. The modified implementation of Bernstein-Vazirani algorithm using polarizers can also be a cost-effective demonstration in an undergraduate lab.

Ro Jefferson

The black hole information paradox is a contradiction between fundamental principles which has puzzled physicists for over forty years. The crux of the problem lies in an assumption about the structure of entanglement across the event horizon, namely, that the Hilbert space factorizes. While valid in quantum mechanics, this fails drastically in quantum field theory, and hence a deeper understanding of entanglement is required if further progress is to be made. Recently, ideas from algebraic quantum field theory have provided new insight into this issue, and show promise for elucidating the connection between entropy and horizons that underlies black hole thermodynamics.