Quantum mechanics and quantum information pdf

Quantum mechanics QM is the part of physics that tells us how the things that make up atoms work. QM also tells us how electromagnetic waves like light work. QM is a mathematical framework rules written in math for much of modern physics and chemistry. Quantum mechanics helps us make sense of the smallest things in nature like protonsneutrons and electrons.

Complex mathematics is used to study subatomic particles and electromagnetic waves because they act in very strange ways. Quantum mechanics is important to physics and chemistry. Quantum is a Latin word that means 'how much'. So a quantum of energy is a specific amount of energy. Light sources such as candles or lasers shoot out or "emit" light in bits called photons. Photons are like packets. Each one has a certain little bit of energy.

Photons are particles much smaller than atoms. The more photons a lamp shoots off, the brighter the light. Light is a form of energy that behaves like the waves in water or radio waves. The distance between the top of one wave and the top of the next wave is called a ' wavelength. A light's color depends on its wavelength. Such light cannot be seen by the human eye. Human eyes are not sensitive to infrared light either.

Wavelengths are not always so small. Radio waves have longer wavelengths. The wavelengths for your FM radio can be several meters in length for example, stations transmitting on Each photon has a certain amount of energy related to its wavelength. The shorter the wavelength of a photon, the greater its energy.Quantum entanglement is a physical resource, like energy, associated with the peculiar nonclassical correlations that are possible between separated quantum systems.

quantum mechanics and quantum information pdf

Entanglement can be measured, transformed, and purified. A pair of quantum systems in an entangled state can be used as a quantum information channel to perform computational and cryptographic tasks that are impossible for classical systems.

The general study of the information-processing capabilities of quantum systems is the subject of quantum information theory. See the entries on the Einstein-Podolsky-Rosen argument in quantum theory and the Copenhagen interpretation of quantum mechanics. The dynamics of the theory specifies how properties change in terms of a law of evolution for the state. On the Copenhagen interpretation, such a description is not possible for quantum systems.

Instead, the quantum state of a system should be understood as a catalogue of what an observer has done to the system and what has been observed, and the import of the state then lies in the probabilities that can be inferred in terms of the theory for the outcomes of possible future observations on the system. Einstein rejected this view and proposed a series of arguments to show that the quantum state is simply an incomplete characterization of a quantum system.

These measurements are mutually exclusive: either a position measurement can be performed, or a momentum measurement, but not both simultaneously.

quantum mechanics and quantum information pdf

The subsequent measurement of momentum, say, after establishing a position correlation, will no longer yield any correlation in the momenta of the two particles. It is as if the position measurement disturbs the correlation between the momentum values, and conversely. Apart from this peculiarity that either correlation can be observed, but not both for the same pair of quantum particles, the position and momentum correlations for the quantum particles are exactly like the classical correlations between two billiard balls after a collision.

Attention has recently been called to the obvious but very disconcerting fact that even though we restrict the disentangling measurements to one system, the representative obtained for the other system is by no means independent of the particular choice of observations which we select for that purpose and which by the way are entirely arbitrary.

The second system cannot be steered into a particular quantum state at the whim of the experimenter, but for many copies of the entangled pair, the experimenter can constrain the quantum state of the second system to lie in a chosen set of quantum states, where these states are correlated with the possible outcomes of measurements carried out on the entangled paired systems, or the paired systems plus ancillas.

He found this conclusion sufficiently unsettling to suggest that the entanglement between two separating systems would persist only for distances small enough that the time taken by light to travel from one system to the other could be neglected, compared with the characteristic time periods associated with other changes in the composite system. He speculated that for longer distances the two systems might in fact be in a correlated mixture of quantum states determined by the entangled state.

Bell looked at entanglement in simpler systems than the EPR example: matching correlations between two-valued dynamical quantities, such as polarization or spin, of two separated systems in an entangled state. Free space entanglement of photons has been confirmed in experiments between the Canary Islands of La Palma and Tenerife, a distance of km. See Herbst et al But it was not until the s that physicists, computer scientists, and cryptologists began to regard the non-local correlations of entangled quantum states as a new kind of non-classical physical resource that could be exploited, rather than an embarrassment for quantum mechanics to be explained away.

Suppose Alice and Bob share an entangled pure state of the sort considered by Bell, say two photons in an entangled state of polarization, where Alice has in her possession one of the entangled photons, and Bob has the second paired photon.

Formally, the amount of classical information we gain, on average, when we learn the value of a random variable or, equivalently, the amount of uncertainty in the value of a random variable before we learn its value is represented by a quantity called the Shannon entropy, measured in bits Shannon and Weaver, A random variable is defined by a probability distribution over a set of values. In the case of a binary random variable, with equal probability for each of the two possibilities, the Shannon entropy is one bit, representing maximal uncertainty.

For all other probabilities — intuitively, representing some information about which alternative is more likely — the Shannon entropy is less than one. For the case of maximal knowledge or zero uncertainty about the alternatives, where the probabilities are 0 and 1, the Shannon entropy is zero.

Since information is always embodied in the state of a physical system, we can also think of the Shannon entropy as quantifying the physical resources required to store classical information. Suppose Alice wishes to communicate some classical information to Bob over a classical communication channel such as a telephone line. A relevant question concerns the extent to which the message can be compressed without loss of information, so that Bob can reconstruct the original message accurately from the compressed version.

What happens if we use the quantum states of physical systems to store information, rather than classical states?Scientists needed a new approach that took the wave behavior of the electron into account. He was notorious for his intense dislike of memorizing data and learning from books.

He then worked at Princeton University in the United States but eventually moved to the Institute for Advanced Studies in Dublin, Ireland, where he remained until his retirement in Although quantum mechanics uses sophisticated mathematics, you do not need to understand the mathematical details to follow our discussion of its general conclusions.

Thus each wavefunction is associated with a particular energy E. The properties of wavefunctions derived from quantum mechanics are summarized here:. The quantum numbers provide information about the spatial distribution of an electron. Although n can be any positive integer, only certain values of l and m l are allowed for a given value of n.

quantum mechanics and quantum information pdf

The principal quantum number n tells the average relative distance of an electron from the nucleus:. As n increases for a given atom, so does the average distance of an electron from the nucleus. A negatively charged electron that is, on average, closer to the positively charged nucleus is attracted to the nucleus more strongly than an electron that is farther out in space. This means that electrons with higher values of n are easier to remove from an atom.

All wavefunctions that have the same value of n are said to constitute a principal shell because those electrons have similar average distances from the nucleus. As you will see, the principal quantum number n corresponds to the n used by Bohr to describe electron orbits and by Rydberg to describe atomic energy levels. The second quantum number is often called the azimuthal quantum number l.

The value of l describes the shape of the region of space occupied by the electron. For a given atom, all wavefunctions that have the same values of both n and l form a subshell. The regions of space occupied by electrons in the same subshell usually have the same shape, but they are oriented differently in space. Each wavefunction with an allowed combination of nland m l values describes an atomic orbitala particular spatial distribution for an electron.

For a given set of quantum numbers, each principal shell has a fixed number of subshells, and each subshell has a fixed number of orbitals. Asked for: number of subshells and orbitals in the principal shell. Because the shell has four values of lit has four subshells, each of which will contain a different number of orbitals, depending on the allowed values of m l.Citation for this page in APA citation style.

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quantum mechanics and quantum information pdf

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Wilson Stephen Wolfram H. There are presently several " interpretations " of quantum mechanics. Many, perhaps most, are attempts to eliminate the element of chance or indeterminism that is involved in the so-called collapse of the wave function. The Information Interpretation is simply "standard quantum physics" plus information being recorded irreversibly. Unlike the Copenhagen Interpretationwe offer several visualizations of what is going on in quantum reality, The Information Interpretation is based on three simple premises: When you hear or read that electrons are both waves and particles, think " either-or " - first a wave of possibilitiesthen an actual particle.

Quantum Entanglement and Information

In our two-stage model of free willan agent first freely generates alternative possibilitiesthen evaluates them and chooses one, adequately determined by its motives, reasons, desires, etc. First come "free alternatives," then "willed actions.

There is only one world. It is a quantum world. Ontologically it is indeterministic. Epistemically, common sense and experience incline us to see it as deterministic.

Information is not a conserved quantity like energy and mass, despite the view of many mathematical physicists, who generally accept determinism. The universe began in a state of equilibrium with minimal information, and information is being created every daydespite the second law of thermodynamics. Note that despite the Heisenberg principle, quantum mechanical measurements are not always uncertain. When a system is measured prepared in an eigenstate, a subsequent measurement Pauli's measurement of the first kind will find it in the same state with perfect certainty.

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Note that the macromolecules of biology are large enough to stabilize their information structures. DNA has been replicating its essential information for billions of years, resisting equilibrium despite the second law of thermodynamics.

Decoherence theorists say that our failure to see quantum superpositions in the macroscopic world is the measurement problem. There is no separate classical world and no need for a quantum-to-classical transition. Clarifying Wave-Particle Duality. An electron is not both a wave and a particle, think " either-or " first a wave of possibilitiesthen an actual particle.You should work in teams of 4. Please let us know if you have problems forming a team.

Please let us know by email as soon as you have a team and a topic selected for your project. At the end of the semester each team will give a 12 minute oral presentation on their topic in class December 3 and December 5. We will give feedback on these presentations and then each student will prepare an individual paper on that topic. The link below contains some suggestions of broad topics for projects, in some cases together with a pointer to a good starting point for your exploration.

Quantum mechanics

Please feel free to google, use Google Scholar, or search on the quant-ph archive for more information on these or other topics. You should feel free to suggest any topic that you are interested in that is related to the themes of the course, but it should be approved by one of the instructors. Please email me whaley berkeley. Project suggestions You can find more project ideas on the webpage for the Spring iteration of this course. See v.

Stolze and Suter, Quantum Computing: a short course from theory to experiment Physics-oriented introduction with discussion of experimental implementation. Mermin, Quantum Computer Science Introductory. Mathematical background. Strang, Gilbert.

Download: Quantum Computation And Quantum Information 10th Anniversary Edition Pdf.pdf

Linear Algebra and Its Applications Good review of matrix theory and applications. Jordan, Thomas F. Linear operators for Quantum Mechanics Thorough presentation of operators and mathematical structure. On quantum mechanics in general.This is where we can start with an explanation of the basics of quantum mechanics for dummies. Spooky, bizarre and mind-boggling are all understatements when it comes to quantum physics.

Mixed States and Density Matrices: Lecture 21 of Quantum Computation at CMU

Things in the subatomic world of quantum mechanics defy all logic of our macroscopic world. Particles can actually tunnel through walls, appear out of thin air and disappear, stay entangled and choose to behave like waves.

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Quantum mechanics deals with the study of particles at the atomic and subatomic levels. The term was coined by Max Born in Though the theory works to provide accurate predictions of phenomena at the subatomic scales, there is no real understanding of why it works, what it really means or what implications it has for our world picture.

Ergo, the best we can do is present you with the central mystery at the heart of quantum mechanics and show you the way its theoretical structure works to provide real world predictions.

Once you decide to go down the rabbit hole, the wonderland of quantum physics, will keep you enthralled forever. So here we go. As seen by a layman, quantum mechanics appears to be more like a bizarre phenomenon or science fantasy flick, full of jargon and complicated mathematical equations.

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In fact, the truth is even stranger. It is only described by a wavefunction or state vector, that can compute the probability or likelihood of finding a particle. The theory sets fundamental limitations on how accurately we can measure particle parameters, replacing classical determinism with probabilistic determinism.

The theory describes just about every phenomena in nature, ranging from the blueness of the sky to the structure of the molecules that make organic life possible. Quantum mechanics arose as a superior theory, due to the fundamental failure of classical mechanics to describe several atomic phenomena. With the discovery of electron, by J.

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Thomson, in the yearthe whole idea of classical physics was shown to be inapplicable at the atomic level. But this theory was not able to explain the following three critical and world famous experiments. According to the classical theory, a black body any object capable of absorbing radiation at all frequencies and radiating it back would emit infinite amount of energy. This was not found to be true experimentally. The energy emitted by a black body seemed to be a function of its frequency, showing a typical bell shaped curve.

This discretization brought in by energy quanta was a fundamental shift in thinking, inconsistent with classical institution of physicists at the time. When ultraviolet light is shone on certain metal surfaces, electrons are emitted. This phenomenon, whereby electrons in atoms get liberated by the absorption of energy from incident light, is called the photoelectric effect.

Classical electromagnetic theory predicted that the number of electrons emitted and their kinetic energy is dependent on the intensity of light reflected from the surface. However, experiments showed that the energy and number of electrons was a function of frequency. Thus light, which was hitherto known to be a wave, was now known to have a dual character — that of a wave and a particle. Classical electromagnetic theory could not explain the optical line emission or absorption spectra, arising from gases and liquids.

All these phenomenological developments and heuristic theory laid ground for the old quantum theory. It was further amended by scientists like W.

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Heisenberg and E. To understand the quantum realm, you need to unlearn and unplug yourself from classical intuition — which serves us well in the macroscopic world, but is eminently useless in here.

Let us peel off our classical intuition layer by layer.Quantum mechanics. Download PDF. Recommend Documents. Quantum statistical mechanics.

Realism and quantum mechanics. Mathematics for quantum mechanics. Supersymmetric quantum mechanics. Concepts in quantum mechanics. Judging it against similar books, one must therefore be concerned with such aspects as the choice of problems treated, the clarity of presentation and the trend of arguments assessed from the pedagogical point of view.

In all these respects the present work seems to be of high standard. The arrangement of the material follows more or less conventional lines. The first chapters, which are mainly of historical character, precede a description of the formal development of quantum mechanics. The last part of the book is devoted to such applications of quantum theory as perturbation methods, theory of radiation and the treatment of systems with identical particles.

At the end of each chapter the authors present a number of problems to be solved, as well as a gocd selection of books recommended for a more thorough-going study of the problems treated in the text.

References to original papers even in other languages than Americanl dealing with special questions are given in foot-notes, and the reader is encouraged b y explanatory remarks to study these sources. Since textbooks are intended for the education of new generations of scientists, their authors have a particular responsibility as regards notations.

Much could be done to diminigh the existing confusion in this respect if the textbooks would use symbols and units internationally agreed upon and recommended by the International Union of Pure and Applied Physics. This remark arises from the fact t h a t the authors of the present book use the symbol gm for gram instead of g. The beautiful typography of the book, with its clear formulae and drawings, deserves special mention. Stefan Rozentai S.

This volume contains a chapter on atomic spectroscopy p. In the present-day atmosphere of rapidly growing specialization the authors have undertaken the difficult and rather ungrateful task of trying to introduce students of spectroscopy into the whole field.

The a t t e m p t has been markedly successful so far. This volume is well-proportioned, perhaps except for the chapter on atomic spectra which could stand abbreviation. Most advanced students for whom the book has been written would know most of this chapter from an elementary physics course. The various topics of the book are well treated. Of course, not even two co-authors can reasonably be expected to possess personal experience in all parts of the vast field of spectroscopy.

By necessity a book of this type must, therefore, be somewhat conservative in its statements.