Quantum Probability and Applications II

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They want to know why quantum mechanics has the form it does, and they are engaged in an ambitious program to find out. It is called quantum reconstruction, and it amounts to trying to rebuild the theory from scratch based on a few simple principles. The basic premise of the quantum reconstruction game is summed up by the joke about the driver who, lost in rural Ireland, asks a passer-by how to get to Dublin.

Quantum theory was empirically motivated, and its rules were simply ones that seemed to fit what was observed. It uses mathematical formulas that, while tried and trusted, were essentially pulled out of a hat by the pioneers of the theory in the early 20th century.

Quantum Theory - Full Documentary HD

Want to know the probability that the particle will be observed in a particular place? Just calculate the square of the wave function or, to be exact, a slightly more complicated mathematical term , and from that you can deduce how likely you are to detect the particle there.

The probability of measuring some of its other observable properties can be found by, crudely speaking, applying a mathematical function called an operator to the wave function. But this so-called rule for calculating probabilities was really just an intuitive guess by the German physicist Max Born. Neither was supported by rigorous derivation.

Quantum mechanics seems largely built of arbitrary rules like this, some of them — such as the mathematical properties of operators that correspond to observable properties of the system — rather arcane. Einstein launched them both, rather miraculously, in Before Einstein, there was an untidy collection of equations to describe how light behaves from the point of view of a moving observer.

Quantum Theory Rebuilt From Simple Physical Principles

Einstein dispelled the mathematical fog with two simple and intuitive principles: that the speed of light is constant, and that the laws of physics are the same for two observers moving at constant speed relative to one another. Grant these basic principles, and the rest of the theory follows. Not only are the axioms simple, but we can see at once what they mean in physical terms. What are the analogous statements for quantum mechanics?

The eminent physicist John Wheeler once asserted that if we really understood the central point of quantum theory, we would be able to state it in one simple sentence that anyone could understand. One of the first efforts at quantum reconstruction was made in by Hardy, then at the University of Oxford.

PHYS Lecture 9: Quantum

He ignored everything that we typically associate with quantum mechanics, such as quantum jumps, wave-particle duality and uncertainty. Instead, Hardy focused on probability: specifically, the probabilities that relate the possible states of a system with the chance of observing each state in a measurement. Hardy found that these bare bones were enough to get all that familiar quantum stuff back again.

Hardy assumed that any system can be described by some list of properties and their possible values. For example, in the case of a tossed coin, the salient values might be whether it comes up heads or tails. Then he considered the possibilities for measuring those values definitively in a single observation. You might think any distinct state of any system can always be reliably distinguished at least in principle by a measurement or observation.

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This course but demands a lot of time and effort and also offered the opportunity to write a term paper on LaTeX. The course instructor, Prof. He is a dedicated professor and exquisitely delivers difficult topics. He has an excellent teaching style, and all his lectures were pretty impressive. He introduces the issue first, talks about the approach, why the proposal would make sense, and clearly states the assumptions before jumping into the derivation. I initially was worried, doubting how I would get my doubts cleared as this was an online course, and it costs dollars not that easy for me.

Thankfully, the forum was very well maintained, and the TA's were very much quick in responding back and always offered proper guidance. There was also an ample number of exercises and problems to work out and test your understanding. Many of them were time-consuming, but the end result was always beneficial, you really start understanding the topics introduced. I really loved the course and would recommend this course to people who wanted to learn more about Quantum Mechanics. This is an excellent course: puts you on the edge of research in field of quantum sciences.

The idea of ending the course with a research paper is just unique and valuable experience. I'd recommend it for Senior undergraduate students. The depth and quality of this course are outstanding. A lot of work from many very smart people has gone into making this class, as well as 8. Completing this class will make you ready to tackle any historical or current paper in Quantum Mechanics. This course is excellent in terms of every quality. It is structured very well. I was able to follow the material when I study properly.

enertijutad.ml TA's were very helpful. The homework exceeded my expectations and helped me learn much more than I thought it would do. The instructor, Prof. Barton Zwiebach, is a master at teaching and describing the material. Wonderful course, but it is not self passed as quoted. This is a drawback since it is 3.

Actually the course took more 30 hr per week to many students. I will take it again, hope it will be self passed next time will run. It was real fun to do this marathonic course. Highly recommended, particularly if you have enough time to dedicate to it. This is an excellent course. The videos, the notes, the attention provided in the forum, everything is superb. I highly recommend it. Before enrolling, you should know that the course is quite demanding. Firstly you need a rather strong background in mathematics and physics and secondly you need to have enough time to follow it.

It is really worth the effort. Sincerely, I have learned in this course more than in any physics course I have followed, and they have been quite a lot. The syllabus is a kind of mix of different topics sometimes without an apparent relation but from my po…. The syllabus is a kind of mix of different topics sometimes without an apparent relation but from my point of view this is an asset of the course that gives a panorama of basic approximation methods and a final brief review on identical particles perhaps the weakest part.

The title "Applications of Quantum Mechanics" is a little misleading but it is impossible to select a name encompassing all the topics. I am extremely grateful to the instructors and to the people that helped them in the forum. The quantum-logic clock at the U. And the NIST strontium clock, unveiled earlier this year , will be that accurate for 5 billion years—longer than the current age of the Earth.

Such super-sensitive atomic clocks help with GPS navigation, telecommunications and surveying. The precision of atomic clocks relies partially on the number of atoms used. Kept in a vacuum chamber, each atom independently measures time and keeps an eye on the random local differences between itself and its neighbors. If scientists cram times more atoms into an atomic clock, it becomes 10 times more precise—but there is a limit on how many atoms you can squeeze in.

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Entangled atoms would not be preoccupied with local differences and would instead solely measure the passage of time, effectively bringing them together as a single pendulum. That means adding times more atoms into an entangled clock would make it times more precise. Entangled clocks could even be linked to form a worldwide network that would measure time independent of location. Traditional cryptography works using keys: A sender uses one key to encode information, and a recipient uses another to decode the message.

This can be fixed using potentially unbreakable quantum key distribution QKD. In QKD, information about the key is sent via photons that have been randomly polarized. This restricts the photon so that it vibrates in only one plane—for example, up and down, or left to right. The recipient can use polarized filters to decipher the key and then use a chosen algorithm to securely encrypt a message. The secret data still gets sent over normal communication channels, but no one can decode the message unless they have the exact quantum key.

That's tricky, because quantum rules dictate that "reading" the polarized photons will always change their states, and any attempt at eavesdropping will alert the communicators to a security breach. In Switzerland tried out an ID Quantique product to provide a tamper-proof voting system during an election.

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And the first bank transfer using entangled QKD went ahead in Austria in But this system doesn't yet work over large distances. So far, entangled photons have been transmitted over a maximum distance of about 88 miles. A standard computer encodes information as a string of binary digits, or bits.

Quantum computers supercharge processing power because they use quantum bits, or qubits, which exist in a superposition of states—until they are measured, qubits can be both "1" and "0" at the same time. This field is still in development, but there have been steps in the right direction.

The company says these are the world's first commercially available quantum computers. There's also uncertainty over whether the chips display any reliable quantum speedup. This type of microscope fires two beams of photons at a substance and measures the interference pattern created by the reflected beams—the pattern changes depending on whether they hit a flat or uneven surface.

Using entangled photons greatly increases the amount of information the microscope can gather, as measuring one entangled photon gives information about its partner. The Hokkaido team managed to image an engraved "Q" that stood just 17 nanometers above the background with unprecedented sharpness. Similar techniques could be used to improve the resolution of astronomy tools called interferometers, which superimpose different waves of light to better analyze their properties.