Tag: irrespective
Splinterlands: Blockchain’s TCG Powerhouse?
Safety Announces Board Refreshment With the Addition of John D. Farina and Deborah E. Gray
Two New Independent Directors Enhance Extensive Insurance, Finance, Data Privacy and Security, Legal, and Governance Expertise on the Board To File Preliminary Proxy Statement That Includes Proposals to Further Enhance Shareholder Rights BOSTON–(BUSINESS WIRE)–Safety Insurance Group, Inc. (NASDAQ: SAFT) (“Safety” or the “Company”) announced today the appointments of John D. Farina and Deborah E. Gray […]
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Exploring Usability Principles of Efficiency and Self-evidency in Product Development
It was in the final semester when I was pursuing my Bachelor’s degree in psychology that I first heard the phrase, ‘User Experience Design’. Having no prior knowledge about the field, I applied for an Read more
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Twitter Launches Verified NFT Profile Pictures
On January 20, 2022, Twitter launched a new non-fungible token (NFT) feature for its Twitter Blue users – a paid subscription service that gives its users access to premium services. This includes editing published tweets, posting longer videos, reading news without advertisements and more. Twitter Blue will allow people to showcase the NFTs they own by […]
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Is The Dawn Of AI Finally Upon Us?
Hearing about what AI (Artificial Technology) can do for us is something previously only talked about in the realm of science fiction. Now though, this kind of technology is rapidly becoming an integral part of our daily lives and in more ways than one. Of course, there are going to be those aspects of our [...]
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Exponential decay of mutual information for Gibbs states of local Hamiltonians
Quantum 6, 650 (2022).
https://doi.org/10.22331/q-2022-02-10-650The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between distant regions are small. In this work, we consider 1D quantum spin systems with local, finite-range, translation-invariant interactions at any temperature. In this setting, we show that Gibbs states satisfy uniform exponential decay of correlations and, moreover, the mutual information between two regions decays exponentially with their distance, irrespective of the temperature. In order to prove the latter, we show that exponential decay of correlations of the infinite-chain thermal states, exponential uniform clustering and exponential decay of the mutual information are equivalent for 1D quantum spin systems with local, finite-range interactions at any temperature. In particular, Araki's seminal results yields that the three conditions hold in the translation-invariant case. The methods we use are based on the Belavkin-Staszewski relative entropy and on techniques developed by Araki. Moreover, we find that the Gibbs states of the systems we consider are superexponentially close to saturating the data-processing inequality for the Belavkin-Staszewski relative entropy.