Entangling power of quantized chaotic systems

We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a novel and useful characterization of quantum states in higher dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in the Schmidt vectors, and the principal Schmidt vectors can be scarred by the projections of classical periodic orbits onto subspaces. The eigenvalues of the reduced density matrices are sensitive to the degree of wavefunction localization, and are roughly exponentially arranged. We also point out the analogy with decoherence, as reduced density matrices corresponding to subsystems of fully chaotic systems are diagonally dominant.Comment: 21 pages including 9 figs. (revtex

A Protocol for a Pan-Canadian Prospective Observational Study on Active Surveillance or Surgery for Very Low Risk Papillary Thyroid Cancer

BackgroundThe traditional management of papillary thyroid cancer (PTC) is thyroidectomy (total or partial removal of the thyroid). Active surveillance (AS) may be considered as an alternative option for small, low risk PTC. AS involves close follow-up (including regularly scheduled clinical and radiological assessments), with the intention of intervening with surgery for disease progression or patient preference.MethodsThis is a protocol for a prospective, observational, long-term follow-up multi-centre Canadian cohort study. Consenting eligible adults with small, low risk PTC (< 2cm in maximal diameter, confined to the thyroid, and not immediately adjacent to critical structures in the neck) are offered the choice of AS or surgery for management of PTC. Patient participants are free to choose either option (AS or surgery) and the disease management course is thus not assigned by the investigators. Surgery is provided as usual care by a surgeon in an institution of the patient’s choice. Our primary objective is to determine the rate of ‘failure’ of disease management in respective AS and surgical arms as defined by: i) AS arm – surgery for progression of PTC, and ii) surgical arm - surgery or other treatment for disease persistence or progression after completing initial treatment. Secondary outcomes include long-term thyroid oncologic and treatment outcomes, as well as patient-reported outcomes.DiscussionThe results from this study will provide long-term clinical and patient reported outcome evidence regarding active surveillance or immediate surgery for management of small, low risk PTC. This will inform future clinical trials in disease management of small, low risk papillary thyroid cancer.Registration detailsThis prospective observational cohort study is registered on clinicaltrials.gov (NCT04624477), but it should not be considered a clinical trial as there is no assigned intervention and patients are free to choose either AS or surgery