Quantum Depolarizing Channel
A quantum depolarizing channel is a model for quantum noise in quantum systems. The d-dimensional depolarizing channel can be viewed as a completely positive trace-preserving map \Delta_\lambda, depending on one parameter \lambda, which maps a state \rho onto a linear combination of itself and the maximally mixed state, :\Delta_\lambda(\rho)=(1-\lambda)\rho+\fracI. The condition of complete positivity requires \lambda to satisfy the bounds :0\le\lambda\le 1+\frac. Qubit Channel The single qubit depolarizing channel has operator-sum representation on a density matrix \rho given by :\Delta_\lambda(\rho) = \sum_^ K_i \rho K_i^\dagger, where K_i are the Kraus operators given by :K_0 = \sqrt I, K_1 = \sqrt X, K_2 = \sqrt Y, K_3 = \sqrt Z and \ are the Pauli matrices. The trace preserving condition is satisfied by the fact that \sum_K_i ^\dagger K_i = I. Geometrically the depolarizing channel \Delta_\lambda can be interpreted as a uniform contraction of the Bloch sphere, parameteri ...
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Noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arises when the brain receives and perceives a sound. Acoustic noise is any sound in the acoustic domain, either deliberate (e.g., music or speech) or unintended. In contrast, Noise (electronics), noise in electronics may not be audible to the human ear and may require instruments for detection. In audio engineering, noise can refer to the unwanted residual electronic noise signal that gives rise to acoustic noise heard as a Hiss (electromagnetic), hiss. This signal noise is commonly measured using A-weighting or ITU-R 468 noise weighting, ITU-R 468 weighting. In experimental sciences, noise can refer to any random fluctuations of data that hinders perception of a signal. Measurement Sound is measured based on the amplitude and frequency ...
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HSW Theorem
HSW may refer to: * Hall School Wimbledon, in Wimbledon, London, England * Harvard Business School, Stanford Graduate School of Business and Wharton School of the University of Pennsylvania, often considered the three top business schools worldwide and referred to together when referencing their cachet or desirability * Haswell (microarchitecture) * Health and Safety at Work etc. Act 1974, of the United Kingdom * Hellenic Seaways, a Greek ferry operator * Heswall railway station, in England * Historical Society of Washington, D.C. * Howard Scott Warshaw (born 1957), American game designer * HowStuffWorks, a website * HSW International, now Remark Media * HSW Łuczniczka, a stadium in Bydgoszcz, Poland * Hungry Shark World, a video game published by Ubisoft. * Huta Stalowa Wola Huta Stalowa Wola (HSW SA) is a defense contractor that operates a steel mill in the city of Stalowa Wola, Poland. It is a major producer of military equipment and one of the largest heavy construction ma ...
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IEEE Transactions On Information Theory
''IEEE Transactions on Information Theory'' is a monthly peer-reviewed scientific journal published by the IEEE Information Theory Society. It covers information theory and the mathematics of communications. It was established in 1953 as ''IRE Transactions on Information Theory''. The editor-in-chief is Muriel Médard (Massachusetts Institute of Technology). As of 2007, the journal allows the posting of preprints on arXiv. According to Jack van Lint, it is the leading research journal in the whole field of coding theory. A 2006 study using the PageRank network analysis algorithm found that, among hundreds of computer science-related journals, ''IEEE Transactions on Information Theory'' had the highest ranking and was thus deemed the most prestigious. '' ACM Computing Surveys'', with the highest impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citati ...
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Unital Qubit Channels
Unital may refer to: * A unital algebra – an algebra that contains a multiplicative identity element. * A geometric unital – a block design for integer . * A unital algebraic structure, such as a unital magma. * A unital map In abstract algebra, a unital map on a C*-algebra is a map \phi which preserves the identity element: :\phi ( I ) = I. This condition appears often in the context of completely positive maps, especially when they represent quantum operations. ...

Lieb–Thirring Inequality
In mathematics and physics, Lieb–Thirring inequalities provide an upper bound on the sums of powers of the negative eigenvalues of a Schrödinger operator in terms of integrals of the potential. They are named after Elliott H. Lieb, E. H. Lieb and Walter Thirring, W. E. Thirring. The inequalities are useful in studies of quantum mechanics and differential equations and imply, as a corollary, a lower bound on the kinetic energy of N quantum mechanical particles that plays an important role in the proof of stability of matter. Statement of the inequalities For the Schrödinger operator -\Delta+V(x)=-\nabla^2+V(x) on \Reals^n with real-valued potential V(x) : \Reals^n \to \Reals, the numbers \lambda_1\le\lambda_2\le\dots\le0 denote the (not necessarily finite) sequence of negative eigenvalues. Then, for \gamma and n satisfying one of the conditions :\begin \gamma\ge\frac12&,\,n=1,\\ \gamma>0&,\,n=2,\\ \gamma\ge0&,\,n\ge3, \end there exists a constant L_, which only depends on \g ...
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