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Accessible Information
Holevo's theorem is an important limitative theorem in quantum computing, an interdisciplinary field of physics and computer science. It is sometimes called Holevo's bound, since it establishes an upper bound to the amount of information that can be known about a quantum state (accessible information). It was published by Alexander Holevo in 1973. Statement of the theorem Suppose Alice wants to send a classical message to Bob by encoding it into a quantum state, and suppose she can prepare a state from some fixed set \, with the i-th state prepared with probability p_i. Let X be the classical register containing the choice of state made by Alice. Bob's objective is to recover the value of X from measurement results on the state he received. Let Y be the classical register containing Bob's measurement outcome. Note that Y is therefore a random variable whose probability distribution depends on Bob's choice of measurement Measurement is the quantification of attributes of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computing
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of wave-particle duality, both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations Exponential growth, exponentially faster than any modern "classical" computer. Theoretically a large-scale quantum computer could post-quantum cryptography, break some widely used encryption schemes and aid physicists in performing quantum simulator, physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications. The basic unit of information in quantum computing, the qubit (or "quantum bit"), serves the same function as the bit in classical computing. However, unlike a classical bit, which can be in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Channel
In quantum information theory, a quantum channel is a communication channel that can transmit quantum information, as well as classical information. An example of quantum information is the general dynamics of a qubit. An example of classical information is a text document transmitted over the Internet. Terminologically, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. In other words, a quantum channel is just a quantum operation viewed not merely as the reduced dynamics of a system but as a pipeline intended to carry quantum information. (Some authors use the term "quantum operation" to include trace-decreasing maps while reserving "quantum channel" for strictly trace-preserving maps.) Memoryless quantum channel We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanical Entropy
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computation And Quantum Information (book)
''Quantum Computation and Quantum Information'' is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang, regarded as a standard text on the subject. It is informally known as "Mike and Ike", after the candies of that name. The book assumes minimal prior experience with quantum mechanics and with computer science, aiming instead to be a self-contained introduction to the relevant features of both. ( Lov Grover recalls a postdoc disparaging it with the remark, "The book is too elementary – it starts off with the assumption that the reader does not even know quantum mechanics.") The focus of the text is on theory, rather than the experimental implementations of quantum computers, which are discussed more briefly. , the book has been cited over 58,000 times on Google Scholar. In 2019, Nielsen adapted parts of the book for his ''Quantum Country'' project. Table of Contents (Tenth Anniversary Edition) * Chapter 1: Introduction and Over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superdense Coding
In quantum information theory, superdense coding (also referred to as ''dense coding'') is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assumption of sender and receiver pre-sharing an entangled resource. In its simplest form, the protocol involves two parties, often referred to as Alice and Bob in this context, which share a pair of maximally entangled qubits, and allows Alice to transmit two bits (i.e., one of 00, 01, 10 or 11) to Bob by sending only one qubit. This protocol was first proposed by Charles H. Bennett (physicist), Charles H. Bennett and Stephen Wiesner in 1970 Memorial blog post by Or Sattath, with scan of Bennett's handwritten notes from 1970. See als [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing. Etymology The coining of the term ''qubit'' is attributed to Benjamin Schumacher. In the acknow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint Probability Distribution
A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw-Hill Connect. Webp.274/ref> They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as suture (joint), sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally. Joints play a vital role in the human body, contributing to movement, sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Trace
In linear algebra and functional analysis, the partial trace is a generalization of the trace (linear algebra), trace. Whereas the trace is a scalar (mathematics), scalar-valued function on operators, the partial trace is an operator (mathematics), operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics, including consistent histories and the relative state interpretation. Details Suppose V, W are finite-dimensional vector spaces over a field (mathematics), field, with dimensions m and n, respectively. For any space , let L(A) denote the space of linear operators on A. The partial trace over W is then written as , where \otimes denotes the Kronecker product. It is defined as follows: For , let , and , be bases for ''V'' and ''W'' respectively; then ''T'' has a matrix representation : \ \quad 1 \leq k, i \leq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completely Positive Map
In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one that satisfies a stronger, more robust condition. Definition Let A and B be C*-algebras. A linear map \phi: A\to B is called a positive map if \phi maps positive elements to positive elements: a\geq 0 \implies \phi(a)\geq 0. Any linear map \phi:A\to B induces another map :\textrm \otimes \phi : \mathbb^ \otimes A \to \mathbb^ \otimes B in a natural way. If \mathbb^\otimes A is identified with the C*-algebra A^ of k\times k-matrices with entries in A, then \textrm\otimes\phi acts as : \begin a_ & \cdots & a_ \\ \vdots & \ddots & \vdots \\ a_ & \cdots & a_ \end \mapsto \begin \phi(a_) & \cdots & \phi(a_) \\ \vdots & \ddots & \vdots \\ \phi(a_) & \cdots & \phi(a_) \end. We then say \phi is k-positive if \textrm_ \otimes \phi is a positive map and completely positive if \phi is k-positive for all k. Properties * Positive maps are mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Instrument
In quantum physics, a quantum instrument is a mathematical description of a quantum measurement, capturing both the classical and quantum outputs. It can be equivalently understood as a quantum channel that takes as input a quantum system and has as its output two systems: a classical system containing the outcome of the measurement and a quantum system containing the post-measurement state. Definition Let X be a countable set describing the outcomes of a quantum measurement, and let \_ denote a collection of trace-non-increasing completely positive maps, such that the sum of all \mathcal_x is trace-preserving, i.e. \operatorname\left(\sum_x\mathcal_x(\rho)\right)=\operatorname(\rho) for all positive operators \rho. Now for describing a measurement by an instrument \mathcal , the maps \mathcal_x are used to model the mapping from an input state \rho to the output state of a measurement conditioned on a classical measurement outcome x . Therefore, the probability th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy (information Theory)
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable X, which may be any member x within the set \mathcal and is distributed according to p\colon \mathcal\to[0, 1], the entropy is \Eta(X) := -\sum_ p(x) \log p(x), where \Sigma denotes the sum over the variable's possible values. The choice of base for \log, the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannon (unit), shannons"), while base Euler's number, ''e'' gives "natural units" nat (unit), nat, and base 10 gives units of "dits", "bans", or "Hartley (unit), hartleys". An equivalent definition of entropy is the expected value of the self-information of a v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
