Intro to information theory cantors paradise medium. Permanently erasing a file does drowning count as a condition. Mar 30, 2017 the shannon entropy quantifies your uncertainty about a classical random variable. Entropy in classical and quantum information theory william fedus physics department, university of california, san diego. Entropy is a central concept in many different disciplines, and many important applications involving entropy can be viewed as entropy optimization problems. Entanglement entropy since in quantum mechanics we interpret a particle as a wave, we can take a linear combination of physical states. Lieb and mary beth ruskai, using a matrix inequality of elliott h.
To explain data compression, and its connection with entropy. Entropy a guide for the perplexed roman frigg and charlotte werndl. June 2010 contents 1 introduction 1 2 entropy in thermodynamics 2 3 information theory 4 4 statistical mechanics 9 5 dynamical systems theory 18 6 fractal geometry 26 7 conclusion 30 1 introduction entropy is ubiquitous in physics, and it plays important roles in numerous. A to show the explicit dependence on the density operator. However, the concept of shanon entropy shares some intuition with boltzmanns. Spa x a pa logpa 1 in a sense, this formula measures how \unlocalized the probability distribution is. By using the proof technique that establishes the left side of the triangle inequality above, one can show that the strong subadditivity. We have explicitly calculated them for cycle, path, and complete graphs. Altogether, the variety of existing network measures bears great potential. The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where uc tuations and randomness are fundamentally unavoidable. Entropy in classical and quantum information theory. Documents and settingstomekpulpitartykuly na stronke. Probability representation entropy for spinstate tomogram. Basic properties of the relative entropy are proved for this generalization.
To explain some of the basic properties of entropy, both classical and quantum. S 0, for an irreversible process, total entropy increases. Entanglement entropy is a measure of how quantum information is stored in a quantum state. What links here related changes upload file special pages permanent link page. This is a fascinating subject, which arose once the notion of information got precise and quantifyable. Close this message to accept cookies or find out how to manage your cookie settings. Consider the following diffusion equation in 1d with periodic boundary conditions. In the previous lecture, we discussed classical entropy and entropy inequalities. Entropy the clausius inequality forms the basis for the definition of a new property called entropy. Entropy and the second law of thermodynamics the second law of thermodynamics in thermochemistry we have seen that reactions are infl uenced by the comparative enthalpies of reactants and products. Reyeslega 1physics department, syracuse university, syracuse, n. Uncertainty, entropy and decoherence of the damped. Entropy is a central concept in both classical and quantum information theory, measuring the uncertainty and the information content in the state of a physical system. The extension of shannon entropy to the field of quantum mechanical systems described by a density matrix.
Thermodynamics the study of the transformations of energy from one form into another first law. It is obvious that the entropy can be computed by the eigende composition of. For example, let us consider a system with two spins. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy are proved.
In the graph above, the yaxis, hx, represents entropy for a symbol with two possibilities again, binary. In this dissertation we study a class of symmetric conic programming problems with nonlinear convex objective functions in the context of euclidean jordan algebras, which includes the so. Randomness extractors randomness extractors are functions that extract almostuniform bits. Entropy and its inequalities entropy and its inequalities last update. Shannon, who formulated many of the key ideas of information theory. In fact, the mathematical machinery we need to develop quantum infor mation theory is very similar to shannons mathematics typical sequences, random coding. As can be seen in the equation above, for an internally reversible process the cyclic integral of. Pdf from sharmamittal to vonneumann entropy of a graph. Topics in quantum entropy and entanglement elliott lieb princeton university princeton cond mat summer school three lectures july 30,31 2014 elliott lieb topics in quantum entropy and entanglement nr. Web of stories life stories of remarkable people 8,596 views. Shannon entropy this chapter is a digression in information theory. A quantity whose cyclic integral is zero depends on the state only. Timedependent entropy of simple quantum model systems. I argue that hemmo and shenkers arguments fail due to several misunderstandings.
Thus, the method considered in this paper is based on a tradeo. Information from its description page there is shown below. For instance, if the entropy of a quantized eld initially in a squeezed state is close to zero and the atomic inversion is in the collapse region, it is known. Carlen1 department of mathematics, hill center, rutgers university, 110 frelinghuysen road piscataway nj 088548019 usa. Introduction the concept of entropy in information theory describes how much information there is in a signal or event.
This estimates how many epr pairs can be extracted from the. Hot network questions how could a dragonproof toy work. We use cookies to distinguish you from other users and to provide you with a better experience on our websites. In the first place, your uncertainty function has been used in statistical mechanics under that name, so it already has a name. If the random variable is distributed according to probability distribution p then the shannon entropy is. The entropy of entanglement or entanglement entropy is a measure of the degree of quantum. First, it is a measure of the quantum information content of letters in the en. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In this lecture, we discuss several information measures that are important for quantifying the amount of information and correlations that are present in quantum systems. Let us begin with a precise statement of this fact.
If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact web. If the state is expressed as a quantum density matrix, then this entropy can be expressed mathematically as. The concept of the classicallike wehrl entropy is a very informative measure describing the time. Physics department and nanolund, lund university, box 118, 22100 lund, sweden. Quantum data compression consider a message composed of n letters, each chosen at random from the ensemble of. This is a more difficult theorem and was proved in 1973 by elliott h. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage. The bottom line is that entropy change is a measure of reversibility. Doesv on neumann entropy correspond to thermodynamic.
Austrian physicist ludwig boltzmann put entropy into the probabilistic setup of statistical mechanics boltzmann, 1877. Like energy, information can reside in one place or another, it can be transmitted through space, and it can be stored for later use. Information entropy is occasionally called shannons entropy in honor of claude e. It is an incredibly rich theory lying at an intersection of. The concept of the classicallike wehrl entropy is a very informative measure describing the time evolution of a quantum system.
Entropy a guide for the perplexed charlotte werndl. Not all this quantities are equivalent, however, and we will show in the following section that only one of them is particularly adapted to the wigner representation of quantum mechanics. From a physical point of view, information theory has nothing to do with physics. Quantum key recycling with optimal key recycling rate. Pdf the shannon entropy is a common way of measuring conservation of sites in multiple sequence alignments, and has also been. Probability representation entropy tomographic entropy of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed.
318 767 135 39 1371 1045 523 537 1313 1467 17 1146 34 709 364 202 1397 123 309 102 811 1389 252 1570 391 447 363 637 1371 693 518 1498 1186 10 230 188 1122 335 837 1258 1289 962