In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. == The general notion of scalar, vector, and tensor operators == In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M {\displaystyle M} , traveling with a definite center of mass momentum, p z ^ {\displaystyle p{\mathbf {\hat {z}} }} , in the z {\displaystyle z} direction. If we rotate the system by 90 ∘ {\displaystyle 90^{\circ }} about the y {\displaystyle y} axis, the momentum will change to p x ^ {\displaystyle p{\mathbf {\hat {x}} }} , which is in the x {\displaystyle x} direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M {\displaystyle p^{2}/2M} . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p{\mathbf {\hat {x}} }} . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states. In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively. Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, L {\displaystyle {\mathbf {L} }} , and the spin angular momentum, S {\displaystyle {\mathbf {S} }} . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.) Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product L ⋅ S {\displaystyle {\mathbf {L} }\cdot {\mathbf {S} }} of the two vector operators, L {\displaystyle {\mathbf {L} }} and S {\displaystyle {\mathbf {S} }} , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components Q i j = ∑ α q α ( 3 r α , i r α , j − r α 2 δ i j ) . {\displaystyle Q_{ij}=\sum _{\alpha }q_{\alpha }\left(3r_{\alpha ,i}r_{\alpha ,j}-r_{\alpha }^{2}\delta _{ij}\right).} Here, the indices i {\displaystyle i} and j {\displaystyle j} can independently take on the values 1, 2, and 3 (or x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} ) corresponding to the three Cartesian axes, the index α {\displaystyle \alpha } runs over all particles (electrons and nuclei) in the molecule, q α {\displaystyle q_{\alpha }} is the charge on particle α {\displaystyle \alpha } , and r α , i {\displaystyle r_{\alpha ,i}} is the i {\displaystyle i} -th component of the position of this particle. Each term in the sum is a tensor operator. In particular, the nine products r α , i r α , j {\displaystyle r_{\alpha ,i}r_{\alpha ,j}} together form a second rank tensor, formed by taking the outer product of the vector operator r α {\displaystyle {\mathbf {r} }_{\alpha }} with itself. == Rotations of quantum states == === Quantum rotation operator === The rotation operator about the unit vector n (defining the axis of rotation) through angle θ is U [ R ( θ , n ^ ) ] = exp ( − i θ ℏ n ^ ⋅ J ) {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right)} where J = (Jx, Jy, Jz) are the rotation generators (also the angular momentum matrices): J x = ℏ 2 ( 0 1 0 1 0 1 0 1 0 ) J y = ℏ 2 ( 0 i 0 − i 0 i 0 − i 0 ) J z = ℏ ( − 1 0 0 0 0 0 0 0 1 ) {\displaystyle J_{x}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}}\,\quad J_{y}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&i&0\\-i&0&i\\0&-i&0\end{pmatrix}}\,\quad J_{z}=\hbar {\begin{pmatrix}-1&0&0\\0&0&0\\0&0&1\end{pmatrix}}} and let R ^ = R ^ ( θ , n ^ ) {\displaystyle {\widehat {R}}={\widehat {R}}(\theta ,{\hat {\mathbf {n} }})} be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ , n ^ ) ] = 1 1 − i sin θ ℏ n ^ ⋅ J − 1 − cos θ ℏ 2 ( n ^ ⋅ J ) 2 . {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=1\!\!1-{\frac {i\sin \theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} -{\frac {1-\cos \theta }{\hbar ^{2}}}({\hat {\mathbf {n} }}\cdot \mathbf {J} )^{2}.} An operator Ω ^ {\displaystyle {\widehat {\Omega }}} is invariant under a unitary transformation U if Ω ^ = U † Ω ^ U ; {\displaystyle {\widehat {\Omega }}={U}^{\dagger }{\widehat {\Omega }}U;} in this case for the rotation U ^ ( R ) {\displaystyle {\widehat {U}}(R)} , Ω ^ = U ( R ) † Ω ^ U ( R ) = exp ( i θ ℏ n ^ ⋅ J ) Ω ^ exp ( − i θ ℏ n ^ ⋅ J ) . {\displaystyle {\widehat {\Omega }}={U(R)}^{\dagger }{\widehat {\Omega }}U(R)=\exp \left({\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right){\widehat {\Omega }}\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right).} === Angular momentum eigenkets === The orthonormal basis set for total angular momentum is | j , m ⟩ {\displaystyle |j,m\rangle } , where j is the total angular momentum quantum number and m is the magnetic angular momentum quantum number, which takes values −j, −j + 1, ..., j − 1, j. A general state within the j subspace | ψ ⟩ = ∑ m c j m | j , m ⟩ {\displaystyle |\psi \rangle =\sum _{m}c_{jm}|j,m\rangle } rotates to a new state by: | ψ ¯ ⟩ = U ( R ) | ψ ⟩ = ∑ m c j m U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =U(R)|\psi \rangle =\sum _{m}c_{jm}U(R)|j,m\rangle } Using the completeness condition: I = ∑ m ′ | j , m ′ ⟩ ⟨ j , m ′ | {\displaystyle I=\sum _{m'}|j,m'\rangle \langle j,m'|} we have | ψ ¯ ⟩ = I U ( R ) | ψ ⟩ = ∑ m m ′ c j m | j , m ′ ⟩ ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =IU(R)|\psi \rangle =\sum _{mm'}c_{jm}|j,m'\rangle \langle j,m'|U(R)|j,m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D ( j ) | ψ ⟩ {\displaystyle |{\bar {\psi }}\rangle =\sum _{mm'}c_{jm}D_{m'm}^{(j)}|j,m'\rangle \quad \Rightarrow \quad |{\bar {\psi }}\rangle =D^{(j)}|\psi \rangle } For one basis ket: | j , m ¯ ⟩ = ∑ m ′ D ( R ) m ′ m ( j ) | j , m ′ ⟩ {\displaystyle |{\overline {j,m}}\rangle =\sum _{m'}{D(R)}_{m'm}^{(j)}|j,m'\rangle } For the case of orbital angular momentum, the eigenstates | ℓ , m ⟩ {\displaystyle |\ell ,m\rangle } of the orbital angular momentum operator L and solutions of Laplace's equation on a 3d sphere are spherical harmonics: Y ℓ m ( θ , ϕ ) = ⟨ θ , ϕ | ℓ , m ⟩ = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) ! ( ℓ + m ) ! P ℓ m ( cos θ ) e i m ϕ {\displaystyle Y_{\ell }^{m}(\theta ,\phi )=\langle \theta ,\phi |\ell ,m\rangle ={\sqrt {{(2\ell +1) \over 4\pi }{(\ell -m)! \over (\ell +m)!}}}\,P_{\ell }^{m}(\cos {\theta })\,e^{im\phi }} where Pℓm is an associated Legendre polynomial, ℓ is the orbital angular momentum quantum number, and m is the orbital magnetic quantum number which takes the values −ℓ, −ℓ + 1, ... ℓ − 1, ℓ The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below. Spherical harmonics are functions of the polar and azimuthal angles, ϕ and θ respectively, which can be conveniently collected into a unit vector n(θ, ϕ) pointing in the direction of those angles, in the Cartesian basis it is: n ^ ( θ , ϕ ) = cos ϕ sin θ e x + s
Lexical choice
Lexical choice is the subtask of Natural language generation that involves choosing the content words (nouns, non-auxiliary verbs, adjectives, and adverbs) in a generated text. Function words (determiners, for example) are usually chosen during realisation. == Examples == The simplest type of lexical choice involves mapping a domain concept (perhaps represented in an ontology) to a word. For example, the concept Finger might be mapped to the word finger. A more complex situation is when a domain concept is expressed using different words in different situations. For example, the domain concept Value-Change can be expressed in many ways: The temperature rose: the verb rose is used for a Value-Change in temperature which increases the value. The temperature fell: the verb fell is used for a Value-Change in temperature which decreases the value. The rain got heavier: the phrase got heavier is used for a Value-Change in precipitation amount when the precipitation is rain. Sometimes words can communicate additional contextual information, for example: The temperature plummeted: the verb plummeted is used for a Value-Change in temperature which decreases the value, when the change is rapid and large. Contextual information is especially significant for vague terms such as tall. For example, a 2m tall man is tall, but a 2m tall horse is small. == Linguistic perspective == Lexical choice modules must be informed by linguistic knowledge of how the system's input data maps onto words. This is a question of semantics, but it is also influenced by syntactic factors (such as collocation effects) and pragmatic factors (such as context). Hence NLG systems need linguistic models of how meaning is mapped to words in the target domain (genre) of the NLG system. Genre tends to be very important; for example the verb veer has a very specific meaning in weather forecasts (wind direction is changing in a clockwise direction) which it does not have in general English, and a weather-forecast generator must be aware of this genre-specific meaning. In some cases there are major differences in how different people use the same word; for example, some people use by evening to mean 6PM and others use it to mean midnight. Psycholinguists have shown that when people speak to each other, they agree on a common interpretation via lexical alignment; this is not something which NLG systems can yet do. Ultimately, lexical choice must deal with the fundamental issue of how language relates to the non-linguistic world. For example, a system which chose colour terms such as red to describe objects in a digital image would need to know which RGB pixel values could generally be described as red; how this was influenced by visual (lighting, other objects in the scene) and linguistic (other objects being discussed) context; what pragmatic connotations were associated with red (for example, when an apple is called red, it is assumed to be ripe as well as have the colour red); and so forth. == Algorithms and models == A number of algorithms and models have been developed for lexical choice in the research community, for example Edmonds developed a model for choosing between near-synonyms (words with similar core meanings but different connotations). However such algorithms and models have not been widely used in applied NLG systems; such systems have instead often used quite simple computational models, and invested development effort in linguistic analysis instead of algorithm development.
Hoopla (digital media service)
Hoopla Digital is a web and mobile streaming platform launched in 2013 that provides access to a wide range of digital media, including audiobooks, eBooks, comics, manga, music, movies, and TV shows. The service is available to users through participating public libraries, allowing library cardholders to borrow and stream digital media. Hoopla is a division of Midwest Tape. == History == Hoopla was launched in 2013. Its goal was for libraries to provide patrons with access to digital content such as audiobooks, music, movies, and TV shows, without the need for holds or waiting lists. Hoopla's model is a pay-per-use system, which means patrons can borrow items instantly. Since its inception, the service has expanded its offerings to include eBooks and comics. The app was built exclusively for public libraries and their patrons. Hoopla Digital is the only platform that combines all formats and all license models into one convenient app with no platform fees. In 2017, Hoopla became available on Apple TV, Amazon Fire TV, Android TV, and Roku, allowing users to stream content on larger screens. In 2020, Hoopla Flex and Bonus Borrows programs are introduced, enabling libraries to move their one copy/one user titles. At that time, there were 6.5 million library card holders and 2,700+ library partners. In 2021, the BingePass was introduced, offering patrons seven days to access entire collections with just one borrow. In 2022, Apple CarPlay and Android Auto become available, giving users safe and easy access while driving. In 2023, manga joins Hoopla's comic collection, adding 1.5 million titles to Hoopla's offerings. In January 2025, Hoopla introduced a new streaming feature called SeasonPass. Building on the existing BingePass model, SeasonPass allows users to borrow an entire season of a television series with a single borrow. == Business model == Hoopla is free-of-charge for patrons of participating libraries. The content is paid for by library systems, using a "per circulation transaction model". == Content == Hoopla claims to have over 500,000 content titles across six formats, including over 25,000 comic books. As of November 2016, Hoopla's content comprised 35% audiobooks (for which Hoopla has contracts with publishers such as Blackstone Audio, HarperCollins, Simon & Schuster Audio, Tantor Audio, and others), followed by 22% movies (for which Hoopla has motion picture contracts with publishers such as Disney, Lionsgate, Starz, Warner Bros., and others), 19% music, 12% ebooks, 6% comics, and 6% television. One drawback is that Hoopla has few new bestsellers. In February 2025, 404 Media reported that Hoopla's collection includes books created by generative AI with fictional authors and dubious quality. Often not labeled as AI-produced or fact-checked, this AI slop can cost libraries money when checked out by unsuspecting patrons. Libraries like Sacramento Public library have questioned the sustainability of Hoopla's pay-per-use model and have considered transitioning to other digital platforms. === Areas served === Hoopla expanded to serve Australia and New Zealand in June 2021. == Technology == Hoopla content can be borrowed and consumed on the web, or via the native Android or iOS apps. Hoopla broadcasts only in Standard definition unlike most of its competitors such as Kanopy. == Parent company == John Eldred and Jeff Jankowski founded Hoopla's parent company, Midwest Tape, in 1989. Midwest Tape is a library vendor of physical media such as audiobooks, CDs, and DVD/Blu-ray. == Controversy == Hoopla and Midwest Tapes were censured by the Library Freedom Project and Library Futures in a joint statement for hosting what it described as "fascist propaganda", including a recent English translation of A New Nobility of Blood and Soil by Richard Walther Darré of the SS and books related to Holocaust denial, in public library collections without the input from the staff. Criticism was also directed at the inclusion of books on homosexuality, abortion, and vaccines claimed by the Library Freedom Project and Library Futures to be misinformation. On February 17, 2022, Hoopla removed a number of titles after public outcry about Holocaust denial books available on the app under non-fiction. The advocacy groups expressed appreciation for the response, however state that it is "insufficient," as they maintain concerns about the company's practices in selecting materials and lack of transparency.
Contact center telephony
In marketing, contact center telephony is the communication and collaboration system used by businesses to either manage high volumes of inbound queries or outbound telephone calls keeping their workforce or agents productive and in control to serve or acquire customers. This business communication system is an extension of computer telephony integration (CTI). == Overview == The interactions between callers and customer service representatives are supported by the collective system of computers, telephones and the Internet. The shift from CTI to contact center telephony is marked by the sheer change in the customer’s behavior when it comes to communication. Means customers are no longer confined only to voice-based communication i.e. phone to connect with their customer service departments. In addition, they are making use of email, SMS, chat, social media, and other virtual contact channels. This is also the reason for the shift in nomenclature from "call centers" to "contact centers", "contact" being a wider term than "call". Respecting the trend, contact center owners need to adopt unified communication or multi-channel approach to let customers get in touch with them via their preferred communication mediums, either voice or non-voice (data). Cloud-based phone system is a further advancement in the direction as it allows operators to access all the features and benefits of call center telephony over the Web against an affordable & flexible pay-as-you-go subscription model. Thus, in-house infrastructure deployment to manage public switched telephone networks, storage, communication applications, and collaboration servers is no more an obligation. Neither is the need to invest resources for their upgrade, repair, maintenance and security as cloud vendor would be responsible for the same. == India == India, a popular call center business process outsourcing destination, often uses a cloud-based phone system in order to cut operational expenses and downtime, and increase connectivity. == Promotion == Businesses can rely on contact center telephony services to respond to their customers’ queries over phone, email, chat, fax, etc. Integrating it with their customer relationship management tools, entire contact details of customers and their interaction sessions with different customer service representatives can be found at one place. The combination can manage not just sales and marketing but also deliver excellent post-sales customer service or technical support to allow customers derive the most from their products or services. Hence, it’s becoming instrumental in increasing customer satisfaction and loyalty and most of the call center services in India are taking refuge from it. The entire contact center telephony service can be availed by professionals over a browser. Hence, businesses can leverage the concept of BYOD (bring your own device) and mobility and serve their customers well using mobile applications. According to market analysts, BYOD increases satisfaction among workforce, and hence their individual and collective productivity as well. BYOD programme significantly reduces the TCO (total cost of ownership) as professionals prefer to work with their own devices rather than using company-provisioned devices. Next, they tend to be more caring towards such devices and can even shell out money to update and upgrade those when required. Integration of IM, along with audio and video conferencing services helps call center or contact center representatives to get real time assistance from their peers or seniors to resolve any complex issues. They can internally exchange information and knowledge articles as and when required. Real-time call monitoring/barging system can be used by quality assessment team to provide important guidelines to agents to maintain the standard of the service as per industry norms. Integrated recording feature is helpful for internal training and quality purposes to improve productivity and customer satisfaction in equal measures. It also helps in getting business insights and improving products or services to gain deeper penetration into the market.
Open Mashup Alliance
The Open Mashup Alliance (OMA) is a non-profit consortium that promotes the adoption of mashup solutions in the enterprise through the evolution of enterprise mashup standards like EMML. The initial members of the OMA include some large technology companies such as Adobe Systems, Hewlett-Packard, and Intel and some major technology users such as Bank of America and Capgemini. According to Dion Hinchcliffe, "Ultimately, the OMA creates a standardized approach to enterprise mashups that creates an open and vibrant market for competing runtimes, mashups, and an array of important aftermarket services such as development/testing tools, management and administration appliances, governance frameworks, education, professional services, and so on." == Specification development == The initial focus of the OMA is developing EMML, which is a declarative mashup domain-specific language (DSL) aimed at creating enterprise mashups. The EMML language provides a comprehensive set of high-level mashup-domain vocabulary to consume and mash a variety of web data sources. EMML provides a uniform syntax to invoke heterogeneous service styles: REST, WSDL, RSS/ATOM, RDBMS, and POJO. EMML also provides the ability to mix and match diverse data formats: XML, JSON, JDBC, JavaObjects, and primitive types. The OMA website provides the EMML specification, the EMML schema, a reference runtime implementation capable of running EMML scripts, sample EMML mashup scripts, and technical documentation. The OMA is developing EMML under a Creative Commons Attribution No Derivatives license. The eventual objective of the OMA is to submit the EMML specification and any other OMA specifications to a recognized industry standards body.
N-jet
An N-jet is the set of (partial) derivatives of a function f ( x ) {\displaystyle f(x)} up to order N. Specifically, in the area of computer vision, the N-jet is usually computed from a scale space representation L {\displaystyle L} of the input image f ( x , y ) {\displaystyle f(x,y)} , and the partial derivatives of L {\displaystyle L} are used as a basis for expressing various types of visual modules. For example, algorithms for tasks such as feature detection, feature classification, stereo matching, tracking and object recognition can be expressed in terms of N-jets computed at one or several scales in scale space.
End-to-end encryption
End-to-end encryption (E2EE) is a method of implementing a secure communication system where only the sender and intended recipient can read the messages. No one else, including the system provider, telecom providers, Internet providers or malicious actors, can access the cryptographic keys needed to read or send messages. End-to-end encryption prevents data from being read or secretly modified, except by the sender and intended recipients. In many applications, messages are relayed from a sender to some recipients by a service provider. In an E2EE-enabled service, messages are encrypted on the sender's device such that no third party, including the service provider, has the means to decrypt them. The recipients retrieve encrypted messages and decrypt them independently on their own devices. Since third parties cannot decrypt the data being communicated or stored, services with E2EE are better at protecting user data from data breaches and espionage. Computer security experts, digital freedom organizations, and human rights activists advocate for the use of E2EE due to its security and privacy benefits, including its ability to resist mass surveillance. Popular messaging apps like WhatsApp, iMessage, Facebook Messenger, and Signal use end-to-end encryption for chat messages, with some also supporting E2EE of voice and video calls. As of May 2025, WhatsApp is the most widely used E2EE messaging service, with over 3 billion users. Meanwhile, Signal with an estimated 70 million users, is regarded as the current gold standard in secure messaging by cryptographers, protestors, and journalists. Since end-to-end encrypted services cannot offer decrypted messages in response to government requests, the proliferation of E2EE has been met with controversy. Around the world, governments, law enforcement agencies, and child protection groups have expressed concerns over its impact on criminal investigations. As of 2025, some governments have successfully passed legislation targeting E2EE, such as Australia's Telecommunications and Other Legislation Amendment Act (2018) and the Online Safety Act (2023) in the UK. Other attempts at restricting E2EE include the EARN IT Act in the US and the Child Sexual Abuse Regulation in the EU.[1] Nevertheless, some government bodies such as the UK's Information Commissioner's Office and the US's Cybersecurity and Infrastructure Security Agency (CISA) have argued for the use of E2EE, with Jeff Greene of the CISA advising that "encryption is your friend" following the discovery of the Salt Typhoon espionage campaign in 2024. == Definitions == End-to-end encryption is a means of ensuring the security of communications in applications like secure messaging. Under E2EE, messages are encrypted on the sender's device such that they can be decoded only by the final recipient's device. In many non-E2EE messaging systems, including email and many chat platforms, messages pass through intermediaries and are stored by a third party service provider, from which they are retrieved by the recipient. Even if messages are encrypted, they are only encrypted 'in transit', and are thus accessible by the service provider. Server-side disk encryption is also distinct from E2EE because it does not prevent the service provider from viewing the information, as they have the encryption keys and can simply decrypt it. The term "end-to-end encryption" originally only meant that the communication is never decrypted during its transport from the sender to the receiver. For example, around 2003, E2EE was proposed as an additional layer of encryption for GSM or TETRA, in addition to the existing radio encryption protecting the communication between the mobile device and the network infrastructure. This has been standardized by SFPG for TETRA. Note that in TETRA, the keys are generated by a Key Management Centre (KMC) or a Key Management Facility (KMF), not by the communicating users. Later, around 2014, the meaning of "end-to-end encryption" started to evolve when WhatsApp encrypted a portion of its network, requiring that not only the communication stays encrypted during transport, but also that the provider of the communication service is not able to decrypt the communications—maliciously or when requested by law enforcement agencies. Similarly, messages must be undecryptable in transit by attackers through man-in-the-middle attacks. This new meaning is now the widely accepted one. == Motivations == The lack of end-to-end encryption can allow service providers to easily provide search and other features, or to scan for illegal and unacceptable content. However, it also means that content can be read by anyone who has access to the data stored by the service provider, by design or via a backdoor. This can be a concern in many cases where privacy is important, such as in governmental and military communications, financial transactions, and when sensitive information such as health and biometric data are sent. If this content were shared without E2EE, a malicious actor or adversarial government could obtain it through unauthorized access or subpoenas targeted at the service provider. E2EE alone does not guarantee privacy or security. For example, the data may be held unencrypted on the user's own device or accessed through their own app if their credentials are compromised. == Modern implementations == === Messaging === In May 2026, Meta ended support for end-to-end encryption (E2EE) on Instagram, reversing a previous commitment to expand the technology across its messaging services. The company justified the move as a measure to mitigate fraudulent activity and facilitate the detection of harmful content. The decision highlighted a conflict between digital privacy and online safety; while child protection organizations supported the change to better identify predatory behavior, privacy advocates argued that removing E2EE compromises user security. As of 2025, messaging apps like Signal and WhatsApp are designed to exclusively use end-to-end encryption. Both Signal and WhatsApp use the Signal Protocol. Other messaging apps and protocols that support end-to-end encryption include Facebook Messenger, iMessage, Telegram, Matrix, and Keybase. Although Telegram supports end-to-end encryption, it has been criticized for not enabling it by default, instead supporting E2EE through opt-in "secret chats". As of 2020, Telegram did not support E2EE for group chats and no E2EE on its desktop clients. In 2022, after controversy over the use of Facebook Messenger messages in an abortion lawsuit in Nebraska, Facebook added support for end-to-end encryption in the Messenger app. Writing for Wired, technologist Albert Fox Cahn criticized Messenger's approach to end-to-end encryption, which required the user to opt into E2EE for each conversation and split the message thread into two chats which were easy for users to confuse. In December 2023, Facebook announced plans to enable end-to-end encryption by default despite pressure from British law enforcement agencies. As of 2016, many server-based communications systems did not include end-to-end encryption. These systems can only guarantee the protection of communications between clients and servers, meaning that users have to trust the third parties who are running the servers with the sensitive content. End-to-end encryption is regarded as safer because it reduces the number of parties who might be able to interfere or break the encryption. In the case of instant messaging, users may use a third-party client or plugin to implement an end-to-end encryption scheme over an otherwise non-E2EE protocol. === Audio and video conferencing === Signal and WhatsApp use end-to-end encryption for audio and video calls. Since 2020, Signal has also supported end-to-encrypted video calls. In 2024, Discord added end-to-end encryption for audio and video calls, voice channels, and certain live streams. However, they had no plans to implement E2EE for messages. In 2020, after acquiring Keybase, Zoom announced end-to-end encryption would be limited to paid accounts. Following criticism from human rights advocates, Zoom extended the feature to all users with accounts. In 2021, Zoom settled an $85M class action lawsuit over past misrepresentation about end-to-end encryption. The FTC confirmed Zoom previously retained access to meeting keys. === Other uses === Some encrypted backup and file sharing services provide client-side encryption. Nextcloud and MEGA, offer end-to-end encryption of shared files. The term "end-to-end encryption" is sometimes incorrectly used to describe client-side encryption. Some non-E2EE systems, such as Lavabit and Hushmail, have described themselves as offering "end-to-end" encryption when they did not. == Law enforcement and regulation == In 2022, Facebook Messenger came under scrutiny because the messages between a mother and daughter in Nebraska were used to seek criminal charges in an abortion-rel