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García-Pintos LP, del Campo A. Limits to Perception by Quantum Monitoring with Finite Efficiency. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1527. [PMID: 34828225 PMCID: PMC8624899 DOI: 10.3390/e23111527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 11/13/2021] [Accepted: 11/14/2021] [Indexed: 11/16/2022]
Abstract
We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent's perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain.
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Affiliation(s)
- Luis Pedro García-Pintos
- Department of Physics, University of Massachusetts, Boston, MA 02125, USA
- Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST/University of Maryland, College Park, MD 20742, USA
| | - Adolfo del Campo
- Department of Physics, University of Massachusetts, Boston, MA 02125, USA
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
- Donostia International Physics Center, E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
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Retrodiction beyond the Heisenberg uncertainty relation. Nat Commun 2020; 11:5658. [PMID: 33168831 PMCID: PMC7652952 DOI: 10.1038/s41467-020-19495-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Accepted: 10/14/2020] [Indexed: 11/23/2022] Open
Abstract
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for the prediction of “hypothetical future measurements”, and it does not describe the situation where knowledge is available about the system both earlier and later than the time of the measurement. Here, we study what happens under such circumstances with an atomic ensemble containing 1011 rubidium atoms, initiated nearly in the ground state in the presence of a magnetic field. The collective spin observables of the atoms are then well described by canonical position and momentum observables, \documentclass[12pt]{minimal}
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\begin{document}$$[{\hat{x}}_{\text{A}},{\hat{p}}_{\text{A}}]=i\hslash$$\end{document}[x^A,p^A]=iℏ. Quantum non-demolition measurements of \documentclass[12pt]{minimal}
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\begin{document}$${\hat{x}}_{\text{A}}$$\end{document}x^A after time t allow precise estimates of both observables at time t. By means of the past quantum state formalism, we demonstrate that outcomes of measurements of both the \documentclass[12pt]{minimal}
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\begin{document}$${\hat{p}}_{A}$$\end{document}p^A observables can be inferred with errors below the standard quantum limit. The capability of assigning precise values to multiple observables and to observe their variation during physical processes may have implications in quantum state estimation and sensing. If we have access to information about a quantum system both before and after a measurement, we are not in the usual remit of the Heisenberg uncertainty principle anymore. Here, the authors demonstrate that, in such a scenario, one can retrodict position and momentum measurements without being limited by HUR.
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Zhou Z, Li B, Su J, Fan X, Chen L, Tang S, Zheng J, Zhang T, Meng Z, Chen Z, Deng H, Hu J, Zhao J. An artificial intelligence model for the simulation of visual effects in patients with visual field defects. ANNALS OF TRANSLATIONAL MEDICINE 2020; 8:703. [PMID: 32617323 PMCID: PMC7327351 DOI: 10.21037/atm.2020.02.162] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Background This study aimed to simulate the visual field (VF) effects of patients with VF defects using deep learning and computer vision technology. Methods We collected 3,660 Humphrey visual fields (HVFs) as data samples, including 3,263 reliable 24-2 HVFs. The convolutional neural network (CNN) analyzed and converted the grayscale map of reliable samples into structured data. The artificial intelligence (AI) simulations were developed using computer vision technology. In statistical analyses, the pilot study determined 687 reliable samples to conduct clinical trials, and the two independent sample t-tests were used to calculate the difference of the cumulative gray values. Three volunteers evaluated the matching degree of shape and position between the grayscale map and the AI simulation, which was graded from 0 to100 scores. Based on the average ranking, the proportion of good and excellent grades was determined, and thus the reliability of the AI simulations was assessed. Results The reliable samples in the experimental data consisted of 1,334 normal samples and 1,929 abnormal samples. Based on the existing mature CNN model, the fully connected layer was integrated to analyze the VF damage parameters of the input images, and the prediction accuracy of the damage type of the VF defects was up to 89%. By mapping the area and damage information in the VF damage parameter quintuple data set into the real scene image and adjusting the darkening effect according to the damage parameter, the visual effects in patients were simulated in the real scene image. In the clinical validation, there was no statistically significant difference in the cumulative gray value (P>0.05). The good and excellent proportion of the average scores reached 96.0%, thus confirming the accuracy of the AI model. Conclusions An AI model with high accuracy was established to simulate the visual effects in patients with VF defects.
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Affiliation(s)
- Zhan Zhou
- Shenzhen Eye Hospital Affiliated to Jinan University, Shenzhen Eye Institute, Shenzhen, China
| | - Bingbing Li
- The Second Affiliated Hospital of Fujian Medical University, Fujian Province University Engineering Research Center of Assistive Technology for Visual Impairment, Quanzhou, China
| | - Jinyu Su
- The Second Affiliated Hospital of Fujian Medical University, Fujian Province University Engineering Research Center of Assistive Technology for Visual Impairment, Quanzhou, China
| | - Xianming Fan
- Shenzhen Eye Hospital Affiliated to Jinan University, Shenzhen Eye Institute, Shenzhen, China
| | - Liang Chen
- Shenzhen Eye Hospital Affiliated to Jinan University, Shenzhen Eye Institute, Shenzhen, China
| | - Song Tang
- Shenzhen Eye Hospital Affiliated to Jinan University, Shenzhen Eye Institute, Shenzhen, China
| | - Jianqing Zheng
- The Second Affiliated Hospital of Fujian Medical University, Fujian Province University Engineering Research Center of Assistive Technology for Visual Impairment, Quanzhou, China
| | - Tong Zhang
- Shenzhen Eye Hospital Affiliated to Jinan University, Shenzhen Eye Institute, Shenzhen, China
| | - Zhiyong Meng
- The Second Affiliated Hospital of Fujian Medical University, Fujian Province University Engineering Research Center of Assistive Technology for Visual Impairment, Quanzhou, China
| | - Zhimeng Chen
- The Second Affiliated Hospital of Fujian Medical University, Fujian Province University Engineering Research Center of Assistive Technology for Visual Impairment, Quanzhou, China
| | - Hongwei Deng
- Shenzhen Eye Hospital Affiliated to Jinan University, Shenzhen Eye Institute, Shenzhen, China
| | - Jianmin Hu
- The Second Affiliated Hospital of Fujian Medical University, Fujian Province University Engineering Research Center of Assistive Technology for Visual Impairment, Quanzhou, China
| | - Jun Zhao
- Shenzhen Eye Hospital Affiliated to Jinan University, Shenzhen Eye Institute, Shenzhen, China.,School of Optometry Affiliated to Shenzhen University, Shenzhen, China
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