![]() We prove that this definition satisfies all of the axioms, recently put forward by Gour, required for a channel entropy function. Motivated by the fact that the entropy of a state ρ can be formulated as the difference of the number of physical qubits and the “relative entropy distance” between ρ and the maximally mixed state, here we define the entropy of a channel N as the difference of the number of physical qubits of the channel output with the “relative entropy distance” between N and the completely depolarizing channel. Thus, an important goal is to define a consistent and meaningful notion of the entropy of a quantum channel. There is a certain perspective that the most fundamental notion in quantum mechanics is that of a quantum channel, as quantum states, unitary evolutions, measurements, and discarding of quantum systems can each be regarded as certain kinds of quantum channels. Sci.The von Neumann entropy of a quantum state is a central concept in physics and information theory, having a number of compelling physical interpretations. Wigner, E.P., Yanase, M.M.: Information content of distributions. Wehrl, A.: General properties of entropy. Vershynina, A., Carlen, E., Lieb, E.: Strong subadditivity of quantum entropy. Umegaki, H.: Conditional expectation in an operator algebra. Simon, B.: Loewner’s Theorem on Monotone Matrix Functions (Springer, 2019) Ruskai, M.B.: Remarks on Kim’s strong subadditivity matrix inequality: extensions and equality conditions’’. Ruskai, M.B.: Another short and elementary proof of strong subadditivity of quantum entropy. Ruskai, M.B.: “Lieb’s simple proof of concavity of \( \) and remarks on related inequalities” Int. B.: “Inequalities for quantum entropy: a review with conditions for equality” J. Petz, D.: Monotone metrics on matrix spaces. Petz, D.: Quasi-entropies for finite quantum systems. Ohya, M., Petz, D.: Quantum Entropy and Its Use (Springer, 1993) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information (Cambridge University Press, 2000) ![]() Lieb, E.H., Ruskai, M.B.: Some operator inequalities of the Schwarz type. Lieb, E.H., Ruskai, M.B.: Proof of the strong subadditivity of quantum-mechanical entropy. Lieb, E., Ruskai, M.B.: A fundamental property of quantum-mechanical entropy. ![]() Lieb, E.H.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Lesniewski, A., Ruskai, M.B.: Monotone Riemannian metrics and relative entropy on noncommutative probability spaces. Lanford, O., III., Robinson, D.W.: Mean entropy of states in quantum statistical mechanics. Kim, I.: Operator extension of strong subadditivity of entropy. Kiefer, J.: Optimum experimental designs. Jenčová, A., Ruskai, M.B.: A unified treatment of convexity of relative entropy and related trace functions, with conditions for equality. Hiai, F., Ruskai, M.B.: Contraction coefficients for noisy quantum channels. Hasegawa, H.: \(\alpha \)-divergence of the noncommutative information geometry” Rep. 529, 73–140 (AMS, 2010)Įffros, E.G.: “A matrix convexity approach to some celebrated quantum inequalities’’. : Trace inequalities and quantum entropy: an introductory course Contemp. : Topics on Operator Inequalities Sapporo Lecture Notes (1978)Īndo, T.: Concavity of certain maps on positive definite matrices and applications to Hadamard products.
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If you look at RIM's long list of recent acquisitions (there are more than just the ones mentioned above - Dash Mobile, Viigo, Gist, etc.), it appears that RIM has bought the players needed to have a winning team, stacking their roster with some real superstars. Dataviz - While RIM didn't buy DataViz outright, they bought a lot of their talent and assets including Documents To Go, which allows for Word, Excel, Powerpoint creation and editing (the premium version of these apps are included free on the PlayBook).The Astonishing Tribe - Creative geniuses and UI experts who, while arriving a little late on the PlayBook project, helped shape some of the aspects of the user experience and will play a much larger role in this moving ahead (a company called Teknision is responsible for a lot of the user interface design on the PlayBook).Torch Mobile - WebKit browser gurus who fixed up BlackBerry's traditionally poor web browsing experience.QNX - makers of the powerful MicroKernal QNX Neutrino operating system upon which the BlackBerry Tablet OS is built.Some of the acquisitions relevant to the BlackBerry PlayBook include: Over the past few years RIM has been building up its team, acquiring the players it needs to fix their historic weaknesses and "future proof" the company (a term RIM's Co-CEO Jim Balsillie used on their last Earnings Call). Not wanting to lose control of their destiny and be regulated to an Android hardware manufacturer trying to differentiate itself from other Android hardware manufacturers, RIM made the decision to play the game on their own terms. For companies like Motorola, HTC, Samsung and LG, Google's Android operating system has been the life-saving fresh start that has allowed them to compete against Apple's iOS. While much improvement has come to BlackBerry Smartphones over the years and the upcoming BlackBerry 6.1 OS looks to push things even farther, the traditional BlackBerry OS on phones is hitting a point of maturity where RIM's only option is to start with something new. Research In Motion is going through a major transition right now. Intro - Getting Ready to Play Ball With the PlayBook Overall BlackBerry Tablet OS Impressions.BlackBerry App World, 3rd Party Apps, and Apps on Android.BlackBerry Bridge and Native Email, PIM, and BBM.Homescreen Experience, Gesture-Based Navigation & UI.Bluetooth Fun: Controlling the PlayBook w/ Mouse and Keyboard.Touchscreen Display and HD Aspect Ratio.BlackBerry PlayBook Hardware Impressions. ![]() BlackBerry PlayBook Key Features & Specifications.BlackBerry PlayBook Review Unit Unboxing Video.Intro - Getting Ready to Play Ball With the PlayBook.Does the PlayBook have what it takes to crank out a homerun? Read our full review to find out! RIM hopes to leverage their success in smartphones and emerge as a major competitor in the tablet game when it steps up to the plate. But pre-release hype is one thing and real-world performance is another. Heck, it even won the first ever Tablet World Series before it was ever released. 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There is only one Lava Flow vape juice flavor. Thus, you will feel its awesomeness after a puff or two. Additionally, it has a tropical island flavor that makes it smooth for your taste buds. What Does Lava Flow Vape Juice Taste Like?Ī sweet exotic taste of pineapple, coconut, and strawberry is how lava flow vape juice tastes. These bottle sizes come in different nicotine strengths like 3mg, 6mg, and 12mg. Additionally, they package their e-liquids in 10ml, 50ml (short-fills), 60ml, and 100ml. This company is based in the United States of America and manufactures most of its e-juices using pure fruits. The lava flow is made by Naked 100, which prides itself in making top e-juices in the market. Therefore, you will not experience a loss of taste as the vape juice is near to end on your device. These ingredients ensure that it tastes sweet from the first to the last vape. The lava flow is made using coconut, pineapple, and strawberries with an infusion of the tropical flavor. ![]() This is a vape juice manufactured by Naked 100. In this article, we will review this e-liquid, how it tastes, and how it is made.Ĭontinue reading to learn more. Therefore, if you were searching for more information about Lava Flow vape juice, then today we got you. Using this e-juice will make your taste buds feel the sweet taste of strawberries, pineapples, and coconut on the first puff. The store also offers same-day shipping for orders made before 3 pm and free shipping for orders above £20.Do you want a blend of tropical and fruits in vape juice? Then, look no further as Lava Flow vape juice has these blends that will make your vaping time wonderful. Visit the store today and look through a wide range of products such as disposables, e-liquids, starter kits, tanks, mods, coils, pods, batteries, and vaping accessories. 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Best Voice Recorders for College Lectures – Our Top Picks So, for whatever reason you are considering using a recording device, let us guide you through some of the best voice recorders on the market in 2021. Whether it be an issue that makes rapid note-taking difficult, or perhaps a hearing impairment that makes listening in-person tricky, voice recorders help students overcome these barriers. Recorders also hold great worth to students with disabilities or special educational needs. Only to discover 20 minutes later that you’ve missed the most important part of the module. Or perhaps you’re that student that gets dragged into a round-up of last night’s action in the college bar. Voice recorders are a useful study tool and one that many college students have turned to, to enhance their learning. In this article, we are going to share with you the Best Voice Recorders for College Lectures. ![]() Panic-stricken, you realize you’ve missed the last 15 minutes of your professor explaining next week’s assignment. It’s the middle of a college lecture and you suddenly snap out of your trance. ![]() Nevertheless, all content published by Proactive is edited and authored by humans, in line with best practice in regard to content production and search engine optimisation.Ĭryptocurrency investment vehicles dealing in bitcoin and ether saw a marked increase in outflows in the last week, according to data compiled by CoinShares. ![]() Proactive will on occasion use automation and software tools, including generative AI. The team also has access to and use technologies to assist and enhance workflows. Our human content creators are equipped with many decades of valuable expertise and experience. Proactive has always been a forward looking and enthusiastic technology adopter. 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Cosmos network will have many blockchains which can communicate with each other. Cosmos network does not want to be limited by the TPS of a single blockchain. To support the global financial system it will take a lot more than 100K TPS. With a variety of layer 2 solutions Ethereum aims to bring transaction speed to 100K TPS. With 64 shards the transaction speed of Ethereum will be around 1000 TPS. 5s faster than the current block time of 12.5s. The block time in Ethereum will be 12s after migrating to PoS which is just. ![]() Sharding is a known method to horizontally scale the database. By limiting the number of validators the total number of network communications between validators gets fixed.Įthereum 2.0 (PoS based) is solving scalability by using using 64 shard chains. Tendermint limits the number of validator nodes to a specific number which can be set by the users of the network. To support high TPS in a PoS network you will have to compromise on decentralisation to reduce network latency. When targeting high TPS this can be a bottle neck because it will require nodes to have very good CPU configuration and low network latency. Validating smart contract transactions can be expensive since each node has to run the whole code execution to determine the final state of the transaction. On top of the network latency there is the time and cost of validating each transaction. To validate each block each validator communicates with the whole network so latency is proportional to nC2 where N is the number of validators. Communication between nodes is limited by physical laws (speed of transmission, packet size) which brings latency. PoS needs validators to validate blocks and broadcast their vote for validity of the new block to the network. PoS does not solve scalability of blockchains. Many PoS chains are already live including CosmosHub. Ethereum is now migrating from PoW to PoS. Proof of stake (PoS) is another consensus algorithm which is much more energy efficient than PoW. To determine the longest chain you have to wait for the chain you are following to be longer than other competing chains. Finality is probabilistic because PoW follows the longest chain. This limit along with probabilistic finality makes the Bitcoin transaction confirmation time to be around 60 minutes considering a 6 blocks confirmation. The consensus rules secures and maintain the globally accepted state of the blockchain but come at the cost of scalability.īitcoin solves consensus and security by using Proof of work (PoW ) consensus which puts a hard cap of 10 minutes per block. Everyone is allowed to write to the database in a secure way provided they follow the rules of the protocol. Blockchains are distributed databases and need globally distributed nodes to store and maintain the state of the database. The idea behind Cosmos network is to have horizontal scalability. ![]() ![]() All the blockchains will implement IBCI (inter blockchain communication interface) so that they can transfer tokens and data between each other seamlessly. ![]() To create a network of blockchains Cosmos provides CosmosSDK (the application layer) and Tendermint SDK (the network and consensus layer) to give complete tools to launch a public or private blockchain. Tendermint BFT is an open source platform and can be used by any project. Cosmos uses Tendermint BFT which is PoS based consensus algorithm. Cosmos is a network of interoperable blockchains. This is an excellent opportunity for new cardholders to pay down existing debt. ![]() It also offers an introductory 0% APR on balance transfers for 14 months. 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October - December 2014: Online Shopping and Department Stores.April - June 2014: Home Improvement Stores, Furniture Stores, and Bed Bath & Beyond®.January - March 2014: Restaurants and Movie.October - December 2015:, Department Stores, and Clothing Stores.July - September 2015: Home Improvement Stores, Department Stores, and.April - June 2015: Restaurants and Movies.January - March 2015: Gas Stations and Ground Transportation.October - December 2016:, Department Stores and Sam's Club.July - September 2016: Home Improvement Stores and.April - June 2016: Restaurants and Movies.January - March 2016: Gas Stations and Ground Transportation. ![]()
![]() A version of Windows like this didn't exist at the time, so Microsoft needed to build it. Microsoft wanted the best of both worlds, a lightweight and legacy-free OS experience found on Windows 10 Mobile, paired with the versatility and feature-rich nature of Windows 10 desktop, something especially important for Microsoft's Continuum plans on Andromeda. The existing version of Windows 10 was and is not optimized for pocketable devices, and Windows 10 Mobile wasn't adaptable enough or where Microsoft needed it to be for a dual-screen form factor. It became apparent rather quickly that Microsoft needed to build a new, modern version of Windows to fully realize its vision for this device. It was decided early on that Andromeda was not going to be powered by an Intel processor, opting for an ARM chip instead. Microsoft started development on the Andromeda project with the mindset that it was going to be a Windows device. Work on Microsoft's dual-screen phone started picking up steam in early 2016, under the codename Andromeda. Today, I want to detail that journey and talk about what this device would be like had it shipped with Windows back in 2018. ![]() Everything from the shape, size, processor, market positioning, and the operating system would be different by the time the product was publicly announced in October 2019. The dummy prototype hardware featured a more traditional smartphone shape housed in a thin metal chassis with pen support, and I'm told they called this early prototype idea the "Surface Pocket." It appears the powers that be at Microsoft liked the idea, and work began on what would eventually become the Surface Duo soon after.Ī lot would change between those early concept ideas and the final product. In these early internal concepts, Microsoft showcased an adaptable UI that would switch between mobile and desktop experiences when moving between single-screen, dual-screen, and a large external display. If you have specific questions or information about content, the website, and applications, please contact us.Around this time, Microsoft had started conceptualizing the idea of a ( possibly Intel powered) dual-screen pocketable Surface running what would eventually become Windows 10. However, Get Archive LLC does not own each component of the compilation displayed and accessible on the PICRYL website and applications. Get Archive LLC is the owner of the compilation of content that is posted on the PICRYL website and applications, which consists of text, images, audio, video, databases, tags, design, codes, and software ("Content"). Get Archive LLC does not charge permission and license fees for use of any of the content on PICRYL, however, upon request, GetArchive can provide rights clearance for content for a fee. GetArchive believes there are no usage restrictions or limitations put on content in the U.S. ![]() Permission for use, re-use, or additional use of the content is not required. Get Archive LLC, creator of PICRYL, endeavors to provide information that it possesses on the copyright status of the content and to identify any other terms and conditions that may apply to the use of the content, however, Get Archive LLC offers no guarantee or assurance that all pertinent information is provided, or that the information is correct in each circumstance. PICRYL makes the world's public domain media fun to find and easy to use. PICRYL is an AI-driven search & similarity engine. PICRYL is the largest media source for public domain images, scans, and documents. 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