Unsolvability of the Halting Problem in Quantum Dynamics

It is shown that the halting problem cannot be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction when we consider the case when the observer's reference frame is the system that is to be evolved in both pictures. We then show that in order to include the evolution of observer's reference frame in a physically sensible way, the Heisenberg picture with time going backwards yields a correct description.Comment: 4 pages, 3 figure

The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization

Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid. Keywords: minimum-error discrimination, success probability, measurement, POVM elements, Helstrom family of ensembles, convex optimization, conjugate states PACS Nos: 03.67.Hk, 03.65.TaComment: 15 page

The Health Effects of Low Glycemic Index and Low Glycemic Load Interventions on Prediabetes and Type 2 Diabetes Mellitus: A Literature Review of RCTs

(This article belongs to the Special Issue Effect of Dietary Patterns or Eating Habits on Diabetes)Diets with a low glycemic index (GI) and a low glycemic load (GL) can improve glycemic control, blood lipids, blood pressure and BMI in prediabetes and type 2 diabetes (T2DM), but evidence regarding other aspects of cardiometabolic health is limited. We searched the literature for RCTs published from 2013 to 2023 and reviewed the evidence on low-GI/GL diets and their effects on different aspects of health in prediabetes and T2DM, aiming to build a report on all relevant outcomes included in the studies. We included 14 RCTs with 1055 participants, who were mostly middle-aged individuals with T2DM. Interventions were mostly low GI and lasted 1–36 months. Low-GI/GL foods and diets showed benefits in terms of short-term glycemic control, weight and adiposity. Longer-term trials would be necessary to determine whether these benefits persist over time and/or lead to lower CVD risk and mortality. Effects on lipid profile were inconsistent. Some studies also reported positive effects of low-GI/GL interventions on blood pressure, inflammatory biomarkers, renal function and gut microbiota composition. Future trials should focus on some of these novel outcome measures, which may provide important insights into the metabolic effects of low-GI diets on individuals with diabetesThis research received financial support from the Foundation for Science and Technology (FCT) under the projects Food4DIAB (EXPL/BAA-AGR/1382/2021), UIDB/50006/2020 and by AgriFood XXI I&D&I project (NORTE-01-0145-FEDER-000041) co-financed by European Regional Development Fund (ERDF), through the NORTE 2020 (Programa Operacional Regional do Norte 2014/2020).info:eu-repo/semantics/publishedVersio

Relativistic entanglement in single-particle quantum states using Non-Linear entanglement witnesses

In this study, the spin-momentum correlation of one massive spin-1/2 and spin-1 particle states, which are made based on projection of a relativistic spin operator into timelike direction is investigated. It is shown that by using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz transformation would decrease both the amount and the region of entanglement.Comment: 16 pages, 2 figures; to be published in Quantum Inf Process, 10.1007/s11128-011-0289-z (2011

Constructing Entanglement Witness Via Real Skew-Symmetric Operators

In this work, new types of EWs are introduced. They are constructed by using real skew-symmetric operators defined on a single party subsystem of a bipartite dxd system and a maximal entangled state in that system. A canonical form for these witnesses is proposed which is called canonical EW in corresponding to canonical real skew-symmetric operator. Also for each possible partition of the canonical real skew-symmetric operator corresponding EW is obtained. The method used for dxd case is extended to d1xd2 systems. It is shown that there exist Cd2xd1 distinct possibilities to construct EWs for a given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied for each type of EWs. In each step, a large class of quantum PPT states is introduced. It is shown that among them there exist entangled PPT states which are detected by the constructed witnesses. Also the idea of canonical EWs is extended to obtain other EWs with greater PPT entanglement detection power.Comment: 40 page

Minimal measurements of the gate fidelity of a qudit map

We obtain a simple formula for the average gate fidelity of a linear map acting on qudits. It is given in terms of minimal sets of pure state preparations alone, which may be interesting from the experimental point of view. These preparations can be seen as the outcomes of certain minimal positive operator valued measures. The connection of our results with these generalized measurements is briefly discussed

Generalized Second Law of Black Hole Thermodynamics and Quantum Information Theory

We propose a quantum version of a gedanken experiment which supports the generalized second law of black hole thermodynamics. A quantum measurement of particles in the region outside of the event horizon decreases the entropy of the outside matter due to the entanglement of the inside and outside particle states. This decrease is compensated, however, by the increase in the detector entropy. If the detector is conditionally dropped into the black hole depending on the experimental outcome, the decrease of the matter entropy is more than compensated by the increase of the black hole entropy via the increase of the black hole mass which is ultimately attributed to the work done by the measurement.Comment: 5 pages, RevTex, submitted to PR