We study the Quantum Measurement Process in a Stern-Gerlach setup with the spin of a silver atom as the quantum system and the position as the apparatus. The system and the apparatus are treated quantum-mechanically using unitary evolution. The new ingredient in our analysis is the idea that the probes determining the position of the silver atom are limited in resolution. We show using a Wigner matrix that due to the coarseness of the detection process, the pure density matrix appears to evolve to an impure one. We quantify the information gained about the spin in a coarse position measurement.
We compare the roles of the Bures-Helstrom (BH) and Bogoliubov-Kubo-Mori (BKM) metrics in the subject of quantum information geometry. We note that there are two limits involved in state discrimination, which we call the "thermodynamic" limit (of N , the number of realizations going to infinity) and the infinitesimal limit (of the separation of states tending to zero). We show that these two limits do not commute in the quantum case. Taking the infinitesimal limit first leads to the BH metric and the corresponding Cramér-Rao bound, which is widely accepted in this subject. Taking limits in the opposite order leads to the BKM metric, which results in a weaker Cramér-Rao bound. This lack of commutation of limits is a purely quantum phenomenon arising from quantum entanglement. We can exploit this phenomenon to gain a quantum advantage in state discrimination and get around the limitation imposed by the Bures-Helstrom Cramér-Rao (BHCR) bound. We propose a technologically feasible experiment with cold atoms to demonstrate the quantum advantage in the simple case of two qubits.
Systemic lupus erythematosus (SLE) is an autoimmune disease in which the immune system of the patient starts attacking healthy tissues of the body. Lupus Nephritis (LN) refers to the inflammation of kidney tissues resulting in renal failure due to these attacks. The International Society of Nephrology/Renal Pathology Society (ISN/RPS) has released a classification system based on various patterns observed during renal injury in SLE [12]. Traditional methods require meticulous pathological assessment of the renal biopsy and are time-consuming. Recently, computational techniques have helped to alleviate this issue by using virtual microscopy or Whole Slide Imaging (WSI). With the use of deep learning and modern computer vision techniques, we propose a pipeline that is able to automate the process of 1) detection of various glomeruli patterns present in these whole slide images and 2) classification of each image using the extracted glomeruli features.
The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach to the classical cloning process showing how cloning can be realised using Hamiltonians. After writing down a canonical transformation that clones classical states, we show how this can be implemented by Hamiltonian evolution. We then propose an experiment using the tools of nonlinear optics to realise the ideas presented here. Finally, to understand the cloning process in a more realistic context, we introduce statistical mechanical noise to the system and study how this affects the cloning process. While most of our work deals with linear systems and harmonic oscillators, we give some examples of cloning maps on manifolds and show that any system whose configuration space is a group manifold admits a cloning canonical transformation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.