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Introduction - The Basics of Quantum Mechanics

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Introduction - The Basics of Quantum Mechanics

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Quantum mechanics or quantum physics describes the way things(particles) behave at the atomic scale.
Contrary to our reality, everything in the atomic scale behaves differently. That is evrything in the quantum realm is described to be as a wave function. The wave function here is not an actual physical property (e.g. like the waves on water) instead it is an abstract mathematical wave formula that simply describes the properties of quantum objects. To actually get the properties of these quantum objects, the probability of the particle has to be calculated from the wave function. The probability then describes the probability of the existence of the object, such that when it is measured the particles described by the wave function will be found at those probable location. Thus differing from our world where everything is deterministic, everything in the Quantum world is probabilistic in nature.

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Our best basic picture of how particles interact to make the world

What is quantum physics? Put simply, it's the physics that explains how everything works: the best description we have of the nature of the particles that make up matter and the forces with which they interact.

Quantum physics underlies how atoms work, and so why chemistry and biology work as they do. You, me and the gatepost - at some level at least, we're all dancing to the quantum tune. If you want to explain how electrons move through a computer chip, how photons of light get turned to electrical current in a solar panel or amplify themselves in a laser, or even just how the sun keeps burning, you'll need to use quantum physics.

The difficulty - and, for physicists, the fun - starts here. To begin with, there's no single quantum theory. There's quantum mechanics, the basic mathematical framework that underpins it all, which was first developed in the 1920s by Niels Bohr, Werner Heisenberg, Erwin Schrödinger and others. It characterises simple things such as how the position or momentum of a single particle or group of few particles changes over time.

But to understand how things work in the real world, quantum mechanics must be combined with other elements of physics - principally, Albert Einstein's special theory of relativity, which explains what happens when things move very fast - to create what are known as quantum field theories.

Three different quantum field theories deal with three of the four fundamental forces by which matter interacts: electromagnetism, which explains how atoms hold together; the strong nuclear force, which explains the stability of the nucleus at the heart of the atom; and the weak nuclear force, which explains why some atoms undergo radioactive decay.

Over the past five decades or so these three theories have been brought together in a ramshackle coalition known as the " standard model" of particle physics. For all the impression that this model is slightly held together with sticky tape, it is the most accurately tested picture of matter's basic working that's ever been devised. Its crowning glory came in 2012 with the discovery of the Higgs boson, the particle that gives all other fundamental particles their mass, whose existence was predicted on the basis of quantum field theories as far back as 1964.

Conventional quantum field theories work well in describing the results of experiments at high-energy particle smashers such as CERN's Large Hadron Collider, where the Higgs was discovered, which probe matter at its smallest scales. But if you want to understand how things work in many less esoteric situations - how electrons move or don't move through a solid material and so make a material a metal, an insulator or a semiconductor, for example - things get even more complex.

The billions upon billions of interactions in these crowded environments require the development of "effective field theories" that gloss over some of the gory details. The difficulty in constructing such theories is why many important questions in solid-state physics remain unresolved - for instance why at low temperatures some materials are superconductors that allow current without electrical resistance, and why we can't get this trick to work at room temperature.

But beneath all these practical problems lies a huge quantum mystery. At a basic level, quantum physics predicts very strange things about how matter works that are completely at odds with how things seem to work in the real world. Quantum particles can behave like particles, located in a single place; or they can act like waves, distributed all over space or in several places at once. How they appear seems to depend on how we choose to measure them, and before we measure they seem to have no definite properties at all - leading us to a fundamental conundrum about the nature of basic reality.

This fuzziness leads to apparent paradoxes such as Schrödinger's cat, in which thanks to an uncertain quantum process a cat is left dead and alive at the same time. But that's not all. Quantum particles also seem to be able to affect each other instantaneously even when they are far away from each other. This truly bamboozling phenomenon is known as entanglement, or, in a phrase coined by Einstein (a great critic of quantum theory), " spooky action at a distance". Such quantum powers are completely foreign to us, yet are the basis of emerging technologies such as ultra-secure quantum cryptography and ultra-powerful quantum computing.

But as to what it all means, no one knows. Some people think we must just accept that quantum physics explains the material world in terms we find impossible to square with our experience in the larger, "classical" world. Others think there must be some better, more intuitive theory out there that we've yet to discover.

In all this, there are several elephants in the room. For a start, there's a fourth fundamental force of nature that so far quantum theory has been unable to explain. Gravity remains the territory of Einstein's general theory of relativity, a firmly non-quantum theory that doesn't even involve particles. Intensive efforts over decades to bring gravity under the quantum umbrella and so explain all of fundamental physics within one " theory of everything " have come to nothing.

Meanwhile cosmological measurements indicate that over 95 per cent of the universe consists of dark matter and dark energy, stuffs for which we currently have no explanation within the standard model, and conundrums such as the extent of the role of quantum physics in the messy workings of life remain unexplained. The world is at some level quantum - but whether quantum physics is the last word about the world remains an open question. Richard Webb

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Our best basic picture of how particles interact to make the world What is quantum physics? Put simply, it's the physics that explains how everything works: the best description we have of the nature of the particles that make up matter and the forces with which they interact.

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- "Entanglement" is used to describe the correlations between two particles that interact and then separate.
- It is formed from the direct interactions between subatomic particles and these can take numerous forms.
- The state is inseparable when it is in entanglement state.

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Einstein's brilliant mistake: Entangled states - Chad Orzel

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2. One-Time Pad and Key distribution problem

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2. One-Time Pad and Key distribution problem

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- Unbreakable but has a serious key distribution problem.
- QC solves this by generate key using non orthogonal quantum states.
- Impossible for anyone to copy the state during distribution, thus makes it impossible to learn anything about the key.

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- Stated by Wootters, Zurek, and Dieks in 1982

- Theorem: An arbitrary quantum state cannot be duplicated perfectly.
- Proof: Suppose the state of a quantum system A, which we wish to copy, is |ψ⟩A. In order to make a copy, we take a system B with the same state space and initial state

|e⟩B. The initial, or blank, state must be independent of |ψ⟩A, of which we have no prior knowledge. The composite system is then described by the tensor product, and its state is |ψ⟩A|e⟩B.
-  Direct result of the linearity of quantum physics and closely related to another theorem in quantum mechanics.
-  By using this impossibility smartly, unconditionally secure key distribution could be achieved.
-  Specially, we can get the following characteristics about quantum no-cloning theorem:
i.  prevents us from using
classical error correction
techniques on quantum
states.
ii.  quantum states cannot be
measured reliably.
iii.  does not prevent
superluminal communication
via quantum entanglement.
iv.  The no-cloning theorem
prevents us from viewing the
holographic principle for
black holes

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-  Basis for the initial realization of fundamental uncertainties in the ability of an experimenter to measure more than one quantum variable at a time.
-  Attempting to measure an elementary particle’s position to the highest degree of accuracy.

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What is the Heisenberg Uncertainty Principle? - Chad Orzel

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- QKD is used to distribute encryption keys, whose security is based on quantum physics and is thus guaranteed for the long-term.
- It allows for secure key agreement over an untrusted channel where the output key is entirely independent from any input value.
- QKD does not eliminating other cyrptographic properties such authentication but it can be used to build systems with new security properties.
- Quantum Key Distribution Protocol: Bennett and Brassard Protocol (BB84)
- To apply QKD practice, sender and receiver need to find the upper bound of Eve’s information quantitatively, given the observed quantum bit error rate (abbreviated QBER) and other system parameters.
- QKD based on Einstein-Podolsky-Rosen (EPR) : If one of the particles is measured according to the rectilinear basis and found to have a vertical polarization, then the other particle will also be found to have a vertical polarization if it is measured according to the rectilinear basis. If however, the second particle is measured according to the circular basis, it may be found to have either left-circular or right-circular polarization.
- Below is stages of Quantum key distribution:

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https://www.extremetech.com/extreme/287094-quantum-cryptography

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https://www.intechopen.com/books/theory-and-practice-of-cryptography-and-network-security-protocols-and-technologies/introduction-to-quantum-cryptography

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Quantum cryptography is a way to encrypt a message by applying principles of quantum mechanics. The most peculiar characteristics of quantum mechanics are the existence of indivisible quanta and of entangled systems. Both are at the root of Quantum Cryptography which could very well be the first commercial application of quantum physics at the individual quantum level.

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Quantum cryptography works by using quantum key distribution. Quantum key distribution is a method of sending encryption keys using some peculiar behaviors of subatomic particles that have possibility to be completely unbreakable. In quantum cryptography, the key is a stream of photons or light particles. Photons have a property called spin which can be changed when it passes through a filter. By using the spin of photons, the sender and receiver can setup the filter to be 1 or 0.

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The main advantages of quantum cryptography are it can detect unauthorized real-time interception of a private communication because the quantum state changes the existing state. It makes the communication more secure because it is based on fundamental laws of physics instead of using algorithms used today. From the perspective of an attacker, trying to hack a quantum cryptography is virtually impossible. What’s more, it is easy to be implemented in any application that require a strong security. The resources required to maintain is not that very huge considering it granted a very secure type of encryption. Also, the performance of a quantum cryptography will keep evolving continuously meaning that it will surely keep getting better in the future.

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The reason why quantum cryptography is becoming more popular and the demand of its application in the real world is increasing is because of the breakthrough of a quantum computer. Nowadays, companies and governments are in arms against each other to build the first usable quantum computer. This technology brings a whole new ways and ideas to solve a computing problem with ease. The breaking of an encryption would be just a piece of cake. Instead of solving one problem at a time, quantum computing can solve thousand of problems at the same processing speed. Things that usually takes about a hundred of days could take just hours with the help of a quantum computing. However, the current commercial quantum computer is far from being able to do that but who knows what the future holds. Maybe the existence of a quantum cryptography is already here but is kept secret by a top-secret government agencies.  Anyway, the idea of a quantum cryptography is very much welcomed by the security sector to help resist against the attacker who are trying to break an encryption.

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- Originating from University of Oxford
- Quantum-secure cryptographic solutions:
i. System on Chip
ii. SDK
iii. E2E

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I'm thrilled to announce that PQShield has raised £5.5 million in seed funding from Kindred Capital, Crane Venture Partners, Oxford Sciences Innovation and angel investors including Andre Crawford-Brunt, Deutsche Bank's former global head of equities...

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I'm thrilled to announce that PQShield has raised £5.5 million in seed funding from Kindred Capital, Crane Venture Partners, Oxford Sciences Innovation and angel investors including Andre Crawford-Brunt, Deutsche Bank's former global head of equities...

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- Quantum Security Solutions by Design
- Developed Quantum Random Number Generators (QRNGs)
- Products and services:
i. HSM - Cicada
ii. QRNG
iii. C-ITS
iv. QSecure

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HSM - Cicada

In todays connected world, we need to be smarter and more vigilant about protecting the communication channels used by the Internet Of Things.

QRNG

Crypta Labs QRNG products & solutions are here to serve several markets - including the critical infrastructure market where hacks could result in physical harm or fatalities to end-users and expose businesses to significant liabilities.

C-ITS

(Co-operative Intelligent Transport Systems)
Crypta Labs Cicada HSM, providing a secure, hardware environment for the generation and management of private & public keypairs.

QSecure

Crypta Labs has developed the world's ﬁrst quantum-seeded encrypted mobile phone using our quantum technology.

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In todays connected world, we need to be smarter and more vigilant about protecting the communication channels used by the Internet Of Things. Crypta Labs QRNG products & solutions are here to serve several markets - including the critical infrastructure market where hacks could result in physical harm or fatalities to end-users and expose businesses to significant liabilities.

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General explanation on how QKD is working: 

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General explanation on how QKD is working: 

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Quantum Key Distribution: Provably Secure Encryption

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It is very secure because when an unauthorized person reads or copies one photon, its state will automatically change. This change can be detected by the two endpoints. Basically it is impossible to read or copy a message encrypted by using quantum without being detected.

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Quantum cryptography uses a series of photons or light particles to transmit the data from a certain location to another location over a fiber optic cable.
When the receiver gets the message, he compares the measurements of properties of these light particles, the receiver and the sender can determine they nature of the key as well as knowing about its safety.

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1) The sender transmits the light particles through a polarizer that works as a filter. This filter giver randomly one of the four polarizations and bit designations.

2)The light particles reach the receiver. The receiver has to use two beam splitters (Horizontal/vertical or diagonal) to read the polarization of each photon(light particles). The receiver has to guess which beam splitter to use for each photons.

3) Once all the photons reach their destination, the receiver tells the sender about every single beam splitter used for each photon in the sequence the photons were sent. The senders must compare the information to the sequence of polarizers used to sent the key. The photons that have been read using the wrong beam are discarded and the resulting sequence of bits is the key.

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Examples of experiments proving Quantum Theory

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Examples of experiments proving Quantum Theory

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1. Schrodinger's Cat
2. Double Slit experiment

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Quantum superposition describes that (to over simplify things) an object can exist in two places at once. Relating to the wave function where we see that there is a probability of something being in existence means that at one point i.e. before measurement the object does not really have a defined state means that it is effectively in a multiple state at once.

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© Yaakov Fein, Universität Wien

Physicists have long struggled with a perplexing conundrum: Why do tiny particles such as atoms, photons, and electrons behave in ways that bacteria, bees, and bowling balls do not? In a phenomenon called quantum superposition, for example, individual units (say, of light) exist in two states at once. They are both waves and particles, only settling on one or the other if you specifically test for it.

This is not something that will happen to an object like your desk. It won't turn solid when you set your coffee cup on it, or liquid if you try to drink it. Superposition has only been observed in the smallest units of matter, which made physicist Markus Arndt of the University of Vienna curious about where the line is. Does quantum weirdness stop at some particular size? If so, which?

To find out, Arndt and his team created a souped-up version of the famed double-slit experiment (see below), which can show whether individual particles are also behaving like waves. Then they worked their way toward increasingly massive objects. The synthetic molecules Arndt's colleagues at the University of Basel in Switzerland developed for the study are the largest particles ever tested in such an experiment. Each contained as many as 2,000 atoms, according to research published in the journal Nature Physics. The molecules, which have a mouthful of a chemical formula (C ₇₀₇H ₂₆₀F ₉₀₈N ₁₆S ₅₃Zn ₄), "had to be massive, stable, and yet volatile enough to fly in a directed beam," Arndt says.

Next, the scientists built a special instrument, a macromolecule interferometer called the Long-Baseline Universal Matter-​Wave Interferometer, or LUMI. With a baseline length of two meters, it's the longest macromolecule interferometer ever built and is specially tuned to compensate for a number of technical challenges (for example, gravity and the rotation of the Earth).

Inside the interferometer, the team used a nanosecond laser pulse of light to propel the molecules through an ultra-high vacuum tube, which shot them toward a series of slotted barriers to reveal patterns in a screen behind. To Ardnt's delight, the mammoth molecules created the same interference pattern as smaller objects. Though they were particles, they were also acting like waves.

In 1801, physicist Thomas Young conducted the first double-slit experiment, shooting a beam of light toward a barrier with two slits in it. Instead of forming two lines on a screen behind the barrier-in the same way that particles might-the beam formed a pattern of interference as if a wave had been pushed through the two slits. In 1908, Geoffrey Ingram Taylor repeated the experiment using a single photon. Even though the photon was a single particle, the wave interference pattern still appeared. That was strange enough, but then it got really weird: When scientists tracked the individual particles as they move through the slits, the monitored particles abandoned their wave-like state and showed up as two separate lines on the screen. It's as if they knew they were being watched.

The push and pull between what we know of the quantum and classical worlds has perplexed physicists for nearly a century. Concepts such as superposition are cornerstones of quantum physics. "And yet, we never find ourselves in such states that we colloquially describe as an object being in two positions at once," Arndt says.

In the hunt for a connection between the quantum and classical world, Arndt aims to push the limits even further, testing larger and more massive particles. "Why not see how far you can go?" physicist Herman Batelaan of the University of Nebraska-Lincoln, who was not involved in the study, tells Popular Mechanics. "It's a beautiful motivation to do this work."

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© Yaakov Fein, Universität Wien Physicists have long struggled with a perplexing conundrum: Why do tiny particles such as atoms, photons, and electrons behave in ways that bacteria, bees, and bowling balls do not? In a phenomenon called quantum superposition, for example, individual units (say, of light) exist in two states at once.

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Quantum entanglement is another weird thing a quantum object exerts. To put it in a way (over simplifying things), quantum entanglement is where two quantum objects are created or pair of them, they share same properties. Meaning that if one object were to be placed at one point in the universe and we measure the other i.e. collapse it the other object will also be correlated with it, meaning that it is somehow connected to the other object at the other end of the universe. This is relating to the wave function is when we split them; technically these waves are the same, thus if we collapse them (measure) it will be the same as well.

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1. Quantum cryptography
2. Quantum Computing
3. Quantum Biology - Theoretical

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Quantum computers are computers that leverages the quantum effects i.e. quantum superposition in order to work. It is said that quantum computers have the upper hand in solving complex mathematical formula, which in the case of modern cryptography (uses complex mathematical formulas) is a bad thing.

How it works : the basics
Normal computers rely on bits to operate. This describes the information or data. And all processing is done in this manner i.e. 0's and 1's. Quantum computers however uses what is called the Qubit. The qubits still have the value of 1's and 0's, the difference is that it can also be in a state where it is both 1 and 0 at the same time. Because of this, quantum computers have the ability to calculate multiple outcomes all at the same time as a result of multiple concurrent states at the same time.

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This is the first in a series of explainers on quantum technology. The other two are on quantum communication and post-quantum cryptography.
A quantum computer harnesses some of the almost-mystical phenomena of quantum mechanics to deliver huge leaps forward in processing power. Quantum machines promise to outstrip even the most capable of today's-and tomorrow's-supercomputers.

They won't wipe out conventional computers, though. Using a classical machine will still be the easiest and most economical solution for tackling most problems. But quantum computers promise to power exciting advances in various fields, from materials science to pharmaceuticals research. Companies are already experimenting with them to develop things like lighter and more powerful batteries for electric cars, and to help create novel drugs.

The secret to a quantum computer's power lies in its ability to generate and manipulate quantum bits, or qubits.

What is a qubit?

Today's computers use bits-a stream of electrical or optical pulses representing 1s or 0 s. Everything from your tweets and e-mails to your iTunes songs and YouTube videos are essentially long strings of these binary digits.

Quantum computers, on the other hand, use qubits, which are typically subatomic particles such as electrons or photons. Generating and managing qubits is a scientific and engineering challenge. Some companies, such as IBM, Google, and Rigetti Computing, use superconducting circuits cooled to temperatures colder than deep space. Others, like IonQ, trap individual atoms in electromagnetic fields on a silicon chip in ultra-high-vacuum chambers. In both cases, the goal is to isolate the qubits in a controlled quantum state.

Qubits have some quirky quantum properties that mean a connected group of them can provide way more processing power than the same number of binary bits. One of those properties is known as superposition and another is called entanglement.

What is superposition?

Qubits can represent numerous possible combinations of 1 and 0 at the same time. This ability to simultaneously be in multiple states is called superposition. To put qubits into superposition, researchers manipulate them using precision lasers or microwave beams.

Thanks to this counterintuitive phenomenon, a quantum computer with several qubits in superposition can crunch through a vast number of potential outcomes simultaneously. The final result of a calculation emerges only once the qubits are measured, which immediately causes their quantum state to "collapse" to either 1 or 0.

What is entanglement?

Researchers can generate pairs of qubits that are "entangled," which means the two members of a pair exist in a single quantum state. Changing the state of one of the qubits will instantaneously change the state of the other one in a predictable way. This happens even if they are separated by very long distances.

Nobody really knows quite how or why entanglement works. It even baffled Einstein, who famously described it as "spooky action at a distance." But it's key to the power of quantum computers. In a conventional computer, doubling the number of bits doubles its processing power. But thanks to entanglement, adding extra qubits to a quantum machine produces an exponential increase in its number-crunching ability.

Quantum computers harness entangled qubits in a kind of quantum daisy chain to work their magic. The machines' ability to speed up calculations using specially designed quantum algorithms is why there's so much buzz about their potential.

That's the good news. The bad news is that quantum machines are way more error-prone than classical computers because of decoherence.

What is decoherence?

The interaction of qubits with their environment in ways that cause their quantum behavior to decay and ultimately disappear is called decoherence. Their quantum state is extremely fragile. The slightest vibration or change in temperature-disturbances known as "noise" in quantum-speak-can cause them to tumble out of superposition before their job has been properly done. That's why researchers do their best to protect qubits from the outside world in those supercooled fridges and vacuum chambers.

But despite their efforts, noise still causes lots of errors to creep into calculations. Smart quantum algorithms can compensate for some of these, and adding more qubits also helps. However, it will likely take thousands of standard qubits to create a single, highly reliable one, known as a "logical" qubit. This will sap a lot of a quantum computer's computational capacity.

And there's the rub: so far, researchers haven't been able to generate more than 128 standard qubits (see our qubit counter here). So we're still many years away from getting quantum computers that will be broadly useful.

That hasn't dented pioneers' hopes of being the first to demonstrate "quantum supremacy."

What is quantum supremacy?

It's the point at which a quantum computer can complete a mathematical calculation that is demonstrably beyond the reach of even the most powerful supercomputer.

It's still unclear exactly how many qubits will be needed to achieve this because researchers keep finding new algorithms to boost the performance of classical machines, and supercomputing hardware keeps getting better. But researchers and companies are working hard to claim the title, running tests against some of the world's most powerful supercomputers.

There's plenty of debate in the research world about just how significant achieving this milestone will be. Rather than wait for supremacy to be declared, companies are already starting to experiment with quantum computers made by companies like IBM, Rigetti, and D-Wave, a Canadian firm. Chinese firms like Alibaba are also offering access to quantum machines. Some businesses are buying quantum computers, while others are using ones made available through cloud computing services.

Where is a quantum computer likely to be most useful first?

One of the most promising applications of quantum computers is for simulating the behavior of matter down to the molecular level. Auto manufacturers like Volkswagen and Daimler are using quantum computers to simulate the chemical composition of electrical-vehicle batteries to help find new ways to improve their performance. And pharmaceutical companies are leveraging them to analyze and compare compounds that could lead to the creation of new drugs.

The machines are also great for optimization problems because they can crunch through vast numbers of potential solutions extremely fast. Airbus, for instance, is using them to help calculate the most fuel-efficient ascent and descent paths for aircraft. And Volkswagen has unveiled a service that calculates the optimal routes for buses and taxis in cities in order to minimize congestion. Some researchers also think the machines could be used to accelerate artificial intelligence.

It could take quite a few years for quantum computers to achieve their full potential. Universities and businesses working on them are facing a shortage of skilled researchers in the field-and a lack of suppliers of some key components. But if these exotic new computing machines live up to their promise, they could transform entire industries and turbocharge global innovation.

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This is the first in a series of explainers on quantum technology. The other two are on quantum communication and post-quantum cryptography. A quantum computer harnesses some of the almost-mystical phenomena of quantum mechanics to deliver huge leaps forward in processing power. Quantum machines promise to outstrip even the most capable of today's-and tomorrow's-supercomputers.

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Quantum computers, contrary to popular beliefs is not actually faster than normal computers, it just has the power to do things all at the same time (because of quantum superposition). Because of this they(the quantum computers) can solve very complex mathematical problems such the integer factorization problem.

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The fact that factoring two prime numbers is a very complex and complicated task is what makes modern cryptography secure. That is, if someone would try to break in, they would have to do an impossible amount of calculations. However because quantum computers can do multiple calculations all at the same time, it is possible that it can actually solve this within a practical amount of time.

The Shor's Algorithm
The shor's algorithm is an algorithm used by quantum computers for integer factorization. The time complexity when run on a quantum computer for this algorithm is exponentially faster than the best classical factoring algorithm. This means that modern cryptographic system such as the RSA that leverages complex mathematical problems is bound to be obsolete in the era of quantum computers.

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Modern cryptography leverages the complex mathematical formulas in order to properly function. Such as the RSA crypto system which relies on the sheer complicated nature of the factoring two large prime numbers. However as it was discussed earlier, Quantum computers are good at solving complex mathematical problems.