Erasmus : The key concepts of quantum mechanics events we would describe as:
- Entanglement: both of particles and even molecules
- Quantum Tunnelling
- Quantum teleportation
- Wave Nature of Particles
- Casimir Vacuum Effects
- Entanglement swapping
- Arrow of Time effects
Erasmus : Quantum entanglement describes a composite system whose constituents cannot be described independently. The Quantum state may be measured for the entire system but not for its constituents. The quantum state of a composite system is was expressible as a sum or superposition of its constituents.
Quantum entanglement has been demonstrated photons, electrons, molecules of the size range of C60-C70 fullerene buckyballs, microscopic diamonds and neutrons. Observational measurements of physical properties such as position, spin, momentum, angular momentum or polarisation, performed on entangled particles are found to be appropriately correlated.
Entanglement is broken when the entangled particles lose their coherence through interaction with their environment, in experimental setups this being observational measurement.
A common method of generating entangled particles is so the process of subatomic particle decay, were a pair of particles is generated. This results in a situation where the total momentum, angular momentum, energy, spin or polarisation of the generated particles must be the same before and after the process.
Therefore one daughter particle must be highly correlated with the other daughter particle, resulting in a net zero change in system state. Note this does not mean that the two generated particles are identical. They are correlated not identical. “Singlet states” are a pair of spin entangled particles.
Erasmus : Quantum Superposition is a term used to describe the state of an entangled quantum system as a whole. It appears to an observer that the state of one particle of an entangled pair knows what measurement has been performed on the other particle and with what outcome, even though there is no known means for this information to be transferred between the particles.
Entangled particles retain the property of quantum superposition even though the individual particles may be separated by large distances.
Erasmus : Quantum Tunneling
In classical physics, when a ball is rolled up a hill, if it is moving too slowly, it will stop and roll back, because it doesn’t have enough energy to get over the top of the hill to the other side. In the quantum world, although the ball seems to be a one-sided hill there is a chance of finding it on the other side.
This means there is a probability that a particle possessing insufficient energy to rise over a barrier, may be able to tunnel through it.
Studies of quantum tunneling have revealed another unusual phenomenon. Barriers placed in the path of tunneling particles do not slow the particle down. Particles may be detected on the other side of the barrier that have made the trip in less time than it would take for a particle to traverse an equal distance without a barrier being present.
If the particles are relativistic particles such as photons, the tunneling speed apparently exceeds the speed of light. Further if the thickness of the barrier is increased, the tunneling speed increases.
Here, the "ball" could, in a sense, borrow energy from its surroundings to tunnel through the wall or "roll over the hill", paying it back by making the reflected electrons more energetic than they otherwise would have been.
Quantum tunneling was first noticed in 1927. By 1928, researchers solve the Schrödinger equation for a nuclear model of alpha decay. The calculation showed a relationship between the half-life of the particle in the energy of emission that seemed to correlate directly to the probability of quantum tunneling.
Quantum tunneling through a barrier. The energy of the tunneled particle is the same but the amplitude is decreased.
Quantum tunneling through a barrier. At the origin (x=0), there is a very high, but narrow potential barrier. A significant tunneling effect can be seen.
Tunnel Diodes In Computing Electronics
There are several phenomena that have the same behavior as quantum tunneling, and thus can be accurately described by tunneling. Examples include the tunneling of a classical wave-particle association, evanescent wave coupling (the application of Maxwell's wave-equation to light) and the application of the non-dispersive wave-equation from acoustics applied to "waves on strings".
Evanescent wave coupling, until recently, was only called "tunneling" in quantum mechanics; now it is used in other contexts.
Quantum Tunnelling via Barrier
Erasmus : Quantum teleportation is a process by which quantum information can be transmitted from a sending to a receiving location. By using quantum entangled sending and receiving platforms, qubits (quantum bits) of information can be transported without having to physically transport the underlying particle to which the qubit is normally attached.
Quantum teleportation to date has been demonstrated for small single particles only, using standard communications technologies such as optical fibre cables.
The term teleportation championed in fiction bears no relationship to the concept of quantum teleportation. Quantum teleportation is primarily a form of communication, not of transportation. The maximum recorded distance for quantum teleportation is currently 144 km by Anton Zeilinger between two of the Canary Islands.
Firstly on entangled quantum state or Bell state must be created between two locations: a source and the destination often called an “”Alice and Bob”. In essence, a quantum channel exists between the two sites.
A classical information link must also exist between the two sites before a qubit can be moved. Two classical bits must be transmitted to accompany each qubit. Bell states are most easily shared using photons from lasers, and so quantum teleportation could be done, in principle, through open space.
Information transferred is limited by light speed (i.e. no FTL or superluminal speeds are possible), as a qubit can’t be reconstructed until the accompanying classical bits arrive. The value lies in security encoding of the communication, able to bypass many eavesdropping methods.
Quantum information also possesses other unusual properties. It cannot be copied. It cannot be deleted without deleting both entangled particles. Classical bits can’t be used to encode quantum bits.
- An EPR pair is generated, one qubit sent to location A, the other to B.
- At location A, a Bell measurement of the EPR pair qubit and the qubit to be teleported (the quantum state) is performed, yielding one of four measurement outcomes, which can be encoded in two classical bits of information. Both qubits at location A are then discarded.
- Using the classical channel, the two bits are sent from A to B. (This is the only potentially time-consuming step after step 1, due to speed-of-light considerations.)
As a result of the measurement performed at location A, the EPR pair qubit at location B is in one of four possible states. Of these four possible states, one is identical to the
original quantum state, and the other three are closely related.
Which of these four possibilities actually obtains is encoded in the two classical bits. Knowing this, the qubit at location B is modified in one of three ways, or not at all, to result in a qubit identical to, the qubit that was chosen for teleportation.
Diagram for quantum teleportation of a photon.
The state of one system can be entangled with the state of another system. For instance, one can use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits. This is not cloning.
No well-defined state can be attributed to a subsystem of an entangled state. Cloning is a process whose result is a separable state with identical factors. According to Asher Peres and David Kaiser, the publication of the no-cloning theorem was prompted by a proposal of Nick Herbert for a superluminal communication device using quantum entanglement.
The proper description of quantum teleportation requires a basic mathematical toolset, indeed becomes accessible students with a good grounding in finite-dimensional linear. In particular, the theory of Hilbert spaces and projection matrixes is heavily used. A qubit is described using a two-dimensional complex number-valued vector space (a Hilbert space)
Erasmus : FTL: (Casimir Vacuum and Quantum Tunnelling)
Einstein's equations of special relativity postulate that the speed of light in a (near) vacuum is invariant in inertial frames. If the nature of the vacuum however is altered in experimental setups, something known as the Scharnhorst effect has been predicted to occur.
Such a vacuum can be created by bringing two perfectly smooth metal plates together at near atomic diameter spacing. A photon travelling between such plates has been predicted to go faster than the standard speed of light, by a very small margin.
The effect has not been demonstrated experimentally at this point in time.
Other physicists have claimed to have violated be limitation of the speed of light using an optical phenomenon known as “evanescent modes”. There is considerable controversy over the currents and explanation of these theoretical phenomena.
There has been some appreciation that quantum tunnelling particles may travel at superluminal velocities through barriers, effectively bypassing limitation of the speed of light.
Due to the high speed of light, small width of barriers and difficulty in measuring very small timeframes, objective verification of these phenomena have proved to be a controversial arena.
Entanglement Swapping is a phenomenon that opens up new controversies in quantum mechanics. In this experimental procedure two pairs of entangled photons are produced. One photon from each pair is sent to an observer who we will call Victor.
Of the remaining photons one is sent each of observer Alice and observer Bob. If observer Victor combines his two photons into an entangled state, Alice’s and Bob’s photons are entangled, although they have never interacted or shared any common past.
Casimir Force Mechanism
Experiments showing entanglement swapping were undertaken successfully in 2012.
In 2013, Peres in a modified experiment protocol demonstrated that it was possible to create entanglement between photons that never coexisted in time. This demonstrated the quantum mechanical concept of non-locality applies to particles with separation in space or in time.
Casimir Force effect
Now this is where it gets interesting. If Alice and Bob measure their photons polarisation states before Victor makes his choice and either entangles or separates his two photons, the logic of the situation gives that whether the two photons are entangled can be defined after their photonic soul mates have been observed and measured . (Only Victor has a capacity to affect both separate photons). This phenomenon is known as “delayed choice entanglement swapping.”
Erasmus :This brings us to a final concept. The arrow of time.
An experiment was conducted in a box in which a qubit of information was encoded. The reflected microwave field was used to monitor the quantum state of the qubit. If information was deleted, calculate for the probability of finding the system particular state gives odds of about 50/50.
However calculating backward using a mathematical process called an effect matrix gives a prediction probability of approximately 90%. This is what we call a hindsight prediction retrodiction. This has been interpreted as suggesting that in the quantum world time runs forward or backward.
Dr AXxxxx : I would suggest in the quantum world, this is evidence that time itself does not exist.
Erasmus : indeed! Other scientists have suggested that this confirms time is an emergent phenomenon for internal observers of such a system but is absent for external observers of this system. Another way of summarising is to simply observe that the experimental results suggest that future events can change the past.
This type of thinking has implications in our understanding of the physical world. Many physical phenomena based on the phenomenon of time. Entropy always runs from highest to lowest over time.
But understanding of quantum mechanics challenges our understanding of time and space. Others have proposed that progressive system entanglement between molecules within the thermodynamic system generates the appearance of entropy.
The backdrop for the steady growth of entanglement throughout the universe is, of course, time itself. The physicists stress that despite great advances in understanding how changes in time occur, they have made no progress in uncovering the nature of time itself or why it seems different (both perceptually and in the equations of quantum mechanics) than the three dimensions of space. Popescu calls this “one of the greatest unknowns in physics.”
Kinkajou : so finally old dog after one of the most incredible digressions of this website we finally arrive at our usual starting point. Just what are we doing out there? And just what could we be doing?
Erasmus: So our next step is to look at how human beings have begun to use quantum mechanical concepts in technology.
Erasmus : Okay! We discussed all the concepts inherent in quantum mechanics. These concepts cover areas such as
- Entanglement: both of particles and even molecules
- Quantum Tunnelling
- Quantum teleportation
- Wave Nature of Particles
- Casimir Vacuum Effects
- Entanglement swapping
- Arrow of Time effects
Erasmus : Quantum Computing
Present day computers have a memory made up of bits, where each bit can have a digital value of either one or zero. A quantum computer has a memory structure based on qubits. A single qubit can represent a one, or a zero, or a superposition of any of these states.
Two qubits have four possible combinations of zero and one digital values or any superposition of these four states. Three qubits have eight possible combinations of zero or one digital values or any superposition of these eight states.
Quantum computers obey the Church – Turing hypothesis. This thesis states that a function can be calculated if its values can be found by some purely mechanical process. The corollary of this is that a present day computer with sufficient computational memory and CPU cycles can be made to simulate any quantum algorithm.
The advantages of quantum computing lie with the ability to use novel or new algorithms in computing. Quantum computing algorithms such as “Simon’s algorithm”, “Shor’s algorithm” or “integer factorisation algorithms” have experimentally been shown to run much faster on quantum computing systems than the present world computers.
The Holy Grail of quantum computing is the ability to undertake integer factorisation which is slow and difficult in ordinary computers analysing large integers if they are the product of a few prime numbers. (For example, factoring the products of two 300 digit primes).
The ability to factor these integers delivers the ability to crack many current public key ciphers. In particular the RSA cipher, Diffie Hellman ciphers are susceptible.
These types of in public key ciphers are commonly used to protect secure webpages and protect email by encryption. Breaking the ciphers would have significant consequences for our current digital systems which guarantee electronic privacy and security.
However there are other cryptographic algorithms that are not especially susceptible to improved integer factorisation by quantum computers. These include the McEliece cryptosystem, lattice-based cryptosystems, dihedral hidden subgroup problem crypto algorithms, and even AES – 256 gripped algorithms.
(Note it has been projected that using Grover’s algorithm to break a symmetric secret key algorithm by brute force requires 2n/2 invocations of the underlying cryptographic algorithm, compared with roughly 2n in the classical computing system.
This means that symmetric key lengths are effectively halved. Increased key size would negate any advantages gained by the introduction of quantum computers.
Thus appears the quantum computing can deliver a number of very specific advantages, but which can be negated by the introduction of new security algorithms.
While this is an advantage, it may not justify the need for incredible amounts of investment to deliver computational advances dependent upon the media which they are operating. Advantages are too easily negated by operational changes.
Quantum computing has a long way to go before it becomes mainstream. A substantial amount of research needs to be undertaken and the design of new elements will require substantial investment.
Decoherence at atomic scales is a major problem, as loss of data in memory effectively requires a computer to be reset or can corrupt computational group. Entering data qubits and reading output qubits is difficult. Logic elements and gates need to be designed.
One technology for accessing quantum states has still not emerged as an obvious choice for a basis for quantum computer development.
Super cooling systems, magnetic resonance reading systems, molecular magnets, optical based systems with beam splitters or phase shifters, use of atoms trapped in optical lattices have all been used to achieve qubit manipulation.
Implementation such systems is highly technical and has a long way to go before it becomes mainstream.
Kinkajou: Computational power to the people!
Erasmus : Quantum cryptography
Possible advantages include:
- Quantum key distribution
- Integer factorization by quantum computing methods
- Access to different algorithms for breaking encrypted data
- New security protocols: is impossible to copy quantum entangled data as the very act of reading encoded data changes the state of the data. This can not only detect eavesdropping but can prevent it at as well.
- Stream ciphers as are commonly used in encrypted web data streams may be much more difficult if not impossible to eavesdrop on or to break the encryption of.
- Altered methods of quantum key distribution
Quantum cryptography is based on entangled particle twins. Identical random number sequences can be generated simultaneously by pairs of widely separated twins and can serve as cipher keys equivalent to one-time pads. The security quantum key distribution can be proven mathematically. A secure key can be generated without imposing any restrictions on the abilities of an eavesdropper.
With classical key distribution the key must be kept secure in transit. Quantum keys do not need to be secured, as their entangled nature guarantees that the simple act of reading will change them.
Quantum computing does rely on the presence of sending and receiving platform. Such a platform does not exist in multi-party transactions except between tech uniquely sophisticated agents e.g. two banks establishing intercommunication for financial transactions.
Security and cryptography are important but there are many ways to bypass these systems. Corrupt software, device or memory compromise at the time of platform composition, and especially social engineering are all potent methods of compromising the most clever technologies. As always of the arms race in cryptography continues between adversaries. Every innovation can be met with an innovation from the outside.
Quantum Keys and Computing
Erasmus : Quantum tunnelling
This technology has relevance to the technology we have now as much to the technology we hope to gain. Tunnelling is a source of current leakage in large-scale computer integrated circuits such as CPU chips, and results in substantial power drain and heating effects. Is considered to place a lower limit on how small silicon circuits and computer chips can be made.
Currently most digital devices use processors sensors and memory chips based on 45 to 60 nm processes with some cutting-edge processes reaching down to about 32 nm. In the Ivybridge CPU series, Intel has instigated a process with a 22 nm die for fabrication. 22 nm is the space between discrete components chip. The dielectric layer on the CPU chip for example is only .5 nm thick, literally 2 to 3 atoms.
When construction of the CPU chip can be ruined by single atom being out of place, it becomes no longer possible to create circuits that are both reliable and cost-effective. It is possible you may reach down to 14 nm as the die silicon fabrication.
However it is the quantum mechanical world especially phenomena of quantum tunnelling which will limit how many further performance increases we can attain to miniaturisation.
Indeed it may require another advance such an improved transistor processes, (example the Memristor), to shrink the generation of our new chips. Cooling, especially super cooling is perhaps another method of bypassing chip performance bottlenecks.
Tunnel junction such as Josephson junctions can be created by separating two conductors with a very thin insulator. At very low temperatures, supercurrents which are currents that flow indefinitely long without any voltage being applied can be generated in semiconductors.
The superconducting semiconductors are coupled by weak link or a physical constriction within the insulator. This allows the current to tunnel between the two conductors. These effects have applications in precision measurements of voltages and magnetic fields.
- Before Josephson's prediction, it was only known that normal (i.e. non-superconducting) electrons can tunnel.
A working mechanism of a resonant tunneling diode device, based on the phenomenon of quantum tunneling through the potential barriers.
Erasmus : Tunnel Diode
These are semiconductor devices that allow electric current to flow in one direction much more than the opposite direction. Typically, tunnel diodes can be made much smaller than normal transistors. By utilizing quantum mechanical effects gate voltages on the diode can be reduced substantially, resulting in much lower power usages.
This improves the performance per power unit for integrated circuits as well as making it possible to fabricate much smaller integrated circuit silicon chips. Once tunneling has occurred voltage bias reduces and the tunnel diode functions once again at the diode. Tunnel field effect transistors are outcome product of quantum tunneling technology.
The scanning tunneling microscope allows imaging of individual atoms on the surface of a metal. When the tip of the scanning tunneling microscope’s needle is brought very close to a conducting surface that has a voltage bias, an electron flow between the needle and the surface is generated and this can be measured.
Current flow can be constant by using pizo- electric rods that alter their working height. Surface topography can be mapped by this method giving the impression actually visualizing the surface.
Note that at atomic sizes, the wavelength of light become significant in allowing visualization. Hence the tunneling microscope method allows a different method of visualizing the nanoscopic. STM’s have inaccuracy to about 1000th of a nanometre which is about 1% of atomic diameter.
Resonant Tunnelling Diode
Kinkajou : So what other teechnologies can you tell us about that are based on quantum effects?
Erasmus : Other technologies based on quantum effects include:
- Achieving superluminal velocities or FTL transmission
- quantum wires
- cloaking invisibility and still technology
- quantum optics
- quantum communication
- accessing quantum energy
- room temperature superconductors
- time travel
- battery technology
- solar panels
- biotechnology effects
- meta-materials including sizing meta-materials designed to counter the effects of earthquakes
- ultra-thin soundproof walls
- super lenses capable of capturing details below the wavelength of light
- radioactive decay by the tunnelling of nuclear particles out of the atomic nucleus
- quantum tunnelling effects in room temperature semiconductors/superconductors
- spontaneous DNA mutation, mediated by proton tunnelling can affect the inter strand base par bonds between DNA. If this occurs while the DNA is being replicated the base pairing rule for DNA can be compromised, causing a mutation which is inherited.
- Quantum machines
- new forms of medical imaging in low light situations. Researchers in 2014 successfully imaged objects using entangled photons. One of a pair of entangled photons was allowed to interact with the object.
The other of the pair of entangled photons is used to create the picture. This substantially reduces the amount of energy needed to be transmitted through the object to obtain image. The situation is unusual because the imaging photons have never interacted with the object spatially and can be remote to the object being imaged.
Quantum Computing Applications
Erasmus : The study of entangled systems still has a long way to go. Recent work with multiple (greater than two) entangled photons suggest that different layers of entanglement can exist between the particles . In some systems if the state of one photon is determined, the other two photons become determined as well.
In other systems if one photon is determined, the other two photons can remain superimposed and undetermined. This obviously opens up applications in quantum computing, quantum informatics, and quantum cryptography, but we are still at an early stage of utilising this knowledge.
Quantum conductivity effects are another application where our knowledge is only emerging. The theory predicts that if positively charged nuclei form a perfectly rectangular array, electron wave packets travelling through a series of uniformly spaced barriers of these positively charged nuclei, will have an extremely high conductance. Impurities in the metal will disrupt this conductance.
This suggests that new diode or transistor elements may evolve. Again we’re still an early stage of utilising this knowledge.
Quantum decoherence is one of the major barriers to exploiting the quantum world. Decoherence is irreversible, and needs to be highly controlled if not avoided in the design of quantum circuits. Decoherence times to be range between nanoseconds two seconds at low temperatures.
Optical quantum circuits have even shorter decoherence times, which imposes a barrier on the design and function of quantum circuits is any operation must be completed more quickly than the decoherence time.
We are still attempting to develop new quantum computer structures to bypass the problem of decoherence time. Quantum braid theory with quasiparticles known as anyons have been suggested as a solution. Again we are still at an early stage of utilising knowledge.
Quantum Computing Applications Effects Computing