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The Quantum Coin: A Simple Look at the 2-State Quantum System

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There are many different models that we can use to describe how particles interact with each other in the quantum world.  We can also refer to these models as systems. A system is a set of parts that form a complex whole and has order to it.One of these systems is a two-level or two-state system. This system is sometimes abbreviated as a TLS.

A simple way of picturing this type of system is a coin. A coin is a single object with two sides to it. In the quantum world, the two sides of the coin would have two possible quantum states. A quantum state is a state of a quantized system that is described by a set of quantum numbers. A quantum number is a  number that expresses the value of some property of a particle which occurs in  the quanta

There are several examples of these systems in the quantum world:

Spin. Spin is one of the four basic quantum numbers. It is the intrinsic angular momentum  It defines the spin given to a particle. For the two level system, spin can exists as counter clockwise and clockwise. It can have a value of either +1/2 or -1/2. There is a special name given to these type of particles. They are called fermions. Fermions obey the Pauli Exclusion Principle. This means that no two particles in the same energy level have the same properties or states. Think about the coin, it has a head on one side and a building(or eagle) on the other side.. There are no two same images per coin. This is the same with spin as a two-level system. One particle has a -1/2 spin while the other particle has a +1/2 spin. Protons, neutron, electron, neutrinos, and quarks are all fermions.

The transition  of an atom from an excited state to a ground state . This is not necessarily a quantum system.Because photons are involved, this can be classified as a quantum system and be called an “atom-light” interaction. Using the coin, you have the excited state on one side and the ground state on the other side. The excited state is where the atom jumps to when energy is added. The ground state is the lowest energy level of the atom.

There are two processes that happen between the ground state and the excited state. These processes are absorption and emission. Absorption happens when the atom absorbs a photon . this causes the atom to become excited. Emission happens when the atom falls to ground state and releases a photon. There are actually two types of emission. There is stimulated emission and spontaneous emission. An example of spontaneous emission would be radioactive decay. An example of stimulated emission is a laser.

The difference between the two types of emission is that stimulated emission requires an induced electromagnetic field. This means that an electromagnetic field has to be introduced to the system to cause emission . Spontaneous emission, on the other hand, occurs naturally. With our coin, we can imagine that the coin has been forced to spin or is infinitely flipping, this action demonstrates how absorption and emission are constantly occurring.

The ammonia molecule. The nitrogen of ammonia has two molecular states. These states are “up “and “down”. Once again, on one side of the coin, you have “up” and on the other, you have “down”.These two states are non-degenerate. When something is non-degenerate, it does not have the same quantum energy level. In this situation, when excitation of the molecule happens, vibration is caused by the absorption and re-emission of photons.

This is similar to tossing a slinky back and forth in your hand.This quantum phenomena allows the ammonia molecule to have its pyramidal shape and allows ammonia to be used a source for a special type of  a  laser called a “maser”.MASER stands for  Microwave Amplification of Stimulated Emission of Radiation.

The qubit. The qubit is used in quantum computing. Like the bit that is used in regular computing, the qubit is the unit of quantum information used in quantum computing. Unlike the bit, the qubit can have a 0 and 1 at the same time. A common example of the two states used in the qubit is polarization. On one side of the coin, there is vertical polarization and on the other, horizontal polarization. You have the value of 0 and perhaps horizontal polarization. While, on the other side, you have the value of 1 and vertical polarization.

The qubit reveals an interesting property about our quantum coin. This property is called superposition. This basically means that two states are existing at the same time. This is also called entanglement. Entanglement is when collective properties are shared. In this case, the collective or common property  is polarization; vertical and horizontal.

The doublet. Doublets are spectral lines of an ionized gas that have been split into two lines under the influence of a magnetic field. The doublet would have +1/2 on one side of the coin and -1/2 on the other side of the coin. The doublet reveals another unique feature about our quantum coin.  This feature is called rotational symmetry. This means that , regardless of how you rotate the coin, the value is still ½.

The concept of the two-level or two-state quantum system is being studied more as researchers seek to refine the idea of quantum computing. Though there are systems other than the qubit. The other systems have helped researchers understand how to manipulate and develop the qubit.

Joel Taylor About the Author: Joel Taylor grew up in Siskiyou County, California. He attended Yreka High School in Yreka, California. After that, he attended College of the Siskiyous in Weed, California and then transferred to Southern Oregon University in Ashland, Oregon where he graduated with a Bachelor's of Science in Physics. Since then, he has had his own tutoring and research company. He has also worked at the Maryland Science Center in Baltimore, Maryland. Joel is also a member of the American Physical Society and American Institute of Physics. Follow on Twitter @Joel_a_taylor.

The views expressed are those of the author and are not necessarily those of Scientific American.

Comments 11 Comments

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  1. 1. gmperkins 3:26 pm 02/26/2013

    I have always found it interesting that so many ‘things’ in physics are two sided, up/down, +/-, etc.

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  2. 2. Carlos Solrac 6:02 pm 02/26/2013

    The “Quantum World” is not a place where strange things occur. Quantum Mechanics is a tool to predict, statistically, certain outcomes. QM is a construct much like a handicap book is not a horse race. Furthermore the terms used in Quantum Mechanics such as “spin” or “Hamiltonian loop” do not refer to particles spinning of going in circles -they are just functions, mathematical expressions to help researchers to design experiments. But in order to get funds and make it more interesting physicists and specially science popularizers make people believe the they are talking about real entities.

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  3. 3. Carlos Solrac 6:07 pm 02/26/2013

    Yes, it’s very interesting –it’s call Symmetry.

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  4. 4. jtdwyer 4:20 am 02/27/2013

    This has the beginnings of a nice tutorial but, as a layperson, I think there are several points that may cause (continued) confusion. There is one particular subject in the article that I think requires revision:
    “The qubit reveals an interesting property about our quantum coin. This property is called superposition. This basically means that two states are existing at the same time. This is also called entanglement. Entanglement is when collective properties are shared. In this case, the collective or common property is polarization; vertical and horizontal.”

    I think this statement, at a minimum, should have been written:
    ‘In quantum computing, the qubit is like a bit in electronic computing, except that whatever quantum property is used to represent binary information, it’s value is not just either 0 or 1 – it’s considered to be simultaneously both values until the property is referenced. This effect is called superposition, which means that a quantum property value can only be definitively determined by direct measurement. Prior to detection, the property is said to exist in all potential values simultaneously – analogous to being only probabilistically determinable prior to measurement.

    ‘Entanglement is a form of superposition, in which the potential values are definitively split between two entangled particles. For example, if a single photon’s polarization can be either vertical or horizontal then, for two entangled photons, if the first detected photon’s polarization is vertical then the other’s, whenever detected, must be horizontal.’

    I think there are other cases where complex concepts are not clearly presented (quantum numbers, for example), but this will be about all I can address. Overall – this tutorial overview is a good idea – thanks!

    To explain the suggested statement revision more fully how the original statement might be misleading…

    Briefly, superposition is the idea that quantum systems simultaneously exist in all their potential states until measured (detected), when a single state is manifested. In some cases, there are more than 2 potential states.
    Qubits are considered to have two possible states (0/1).

    The statement “In this case, the collective or common property is polarization; vertical and horizontal” seems to have been taken out of context. In proper context, for example, it’s stated in
    “A qubit is a two-state quantum-mechanical system such as the polarization of a single photon: here the two states are vertical polarization and horizontal polarization.”
    If quantum state properties other than photon polarization are used to represent a qubit, the alternative states would be different.

    I think that superpostion and entanglement are commonly confused – they are not the same thing, as implied in the article. In the terms used in the article, entanglement is when a quantum property’s potential states are split between multiple particles. If a single photon’s polarization can be either vertical or horizontal then, for two entangled photons, if the first detected photon’s polarization is vertical then the other’s, whenever detected, must be horizontal, and vice-versa. As stated in
    “Quantum entanglement is a form of quantum superposition. When a measurement is made and it causes one member of such a pair to take on a definite value (e.g., clockwise spin), the other member of this entangled pair will at any subsequent time be found to have taken the appropriately correlated value (e.g., counterclockwise spin). Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may have been separated by arbitrarily large distances.”

    BTW – personally, I do not accept that the initial detection of one particle physically causes the complementary state of the second to occur where and whenever it is eventually detected, but that is definitely the apparent effect observed experimentally. I’ll spare the reader my personal explanation for now…

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  5. 5. jtdwyer 4:42 am 02/27/2013

    BTW, I should add that, as I understand, some/many consider that a qubit does not just simultaneously represent a value of both 0 and 1 – but all potential values in between! In this way, it’s thought that a single quantum bit (qubit) can contain an infinite amount of information and that quantum operations can therefore access an infinitude of information in a single operation.

    Personally, I don’t know how any meaningful information can be stored as an infinite range of values in a qubit, but then I’m just an old-time mainframer – I’m sure I just don’t understand the amazing potential of this new computing paradigm <%)

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  6. 6. TonyTrenton 6:50 am 02/27/2013

    I think that ;
    All particles have spin. A aggregate spin. That is the resultant of the spinning shells of compressed e.m.f. That are shells within shells, within shells.

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  7. 7. phoenix91125 9:24 am 02/27/2013

    I would like to address some of these comments. First of all, this article is an article that uses an object to explain a two-state system. Second of all, wikipedia, wikismedia, everything in wikipedia is a generalization, nothing should be taken as full belief and therefore can be a bad reference and bad source for an article. The writer may have taken that reference from , oh let’s say physicsworld. Never make an assumption of where a source comes from. When an object is used to demonstrate a concept, there should be only what a reader can handle and nothing more. You do not want to hand the reader a lot to chew, you want them to enjoy it and have them try to imagine what is going on in a two state system. Everyone has a different interpretation.

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  8. 8. phoenix91125 9:53 am 02/27/2013

    I should state that the word “simple” is there for a reason

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  9. 9. jtdwyer 11:55 am 02/27/2013

    phoenix91125 – I’ll address your comment directly, since obviously I’m the only one who referred to Wikipedia. I certainly think the Wikipedia statements I quoted were much more specific (less general) than the statements made in this article.

    What does “nothing should be taken as full belief” mean to you? It makes no sense to me…
    When & where did I mention where the “writer may have taken that reference from?” Unlike my comment, there are no citations or references contained within this article so I could not make any assumptions about where the author got his information. I made no such assumptions. I only got my own information from Wikipedia, which is a freely available source accessible to all. BTW, the cited articles do include formal citations and references, most often from peer reviewed journal articles, not other sites like Physics World.

    The purpose of a tutorial is to inform a casual reader – not to misinform or confuse, or to allow the uninformed the pleasure of imagining their own personal reality.

    The following statements in the revised paragraph were clearly erroneous and/or misleading:
    “This is also called entanglement.
    – superposition is not synonymous with entanglement
    – entanglement is a unique form of superposition
    “Entanglement is when collective properties are shared.”
    – entanglement is when a property’s potential values are split between two particles
    – no mention was made in the text that entanglement even involved two particles
    “In this case, the collective or common property is polarization; vertical and horizontal.”
    – as I understand, only in the case of photons, the particle that mediates the EM force interaction, is the entangled property particle polarization: vertical or horizontal

    IMO, you don’t want to hand the reader a load of BS in a tutorial, do you?

    While my suggested revision to the specific paragraph I addressed was a little longer, I definitely think it was clearer, much more correct and informative. If you want to take issue with any of the suggested specific changes in the revised statement I’ll be happy to discuss them.

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  10. 10. phoenix91125 1:21 pm 02/27/2013

    R,jtdwyer, you and I agree on one thing”The purpose of a tutorial is to inform a casual reader” and I am not arguing with you in any fashion- I do truly believe though that wikipedia is a poor source and not an overall reliable source of information. People contribute to wikipedia articles. One article can consists of several interpretations mixed together. In an odd sense, it can be like the telephone game, but in this case, once the article is done, it is turns out to be something completely different than originally. One good example is an article on tryptophan, wikipedia states that “It is particularly plentiful in chocolate”. Well, we all know that is false, I would hopeso. Once again, not arguing with you, but making my statement that Wikipedia is not reliable. And yes, blogs should be more informative to both the lay person and the intellectual, we can all benefit from them

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  11. 11. cloustonenergy 7:54 pm 10/17/2013

    Two sided or polarized is contained in the symbol of the Yin and Yang. Niels Bohr included this symbol on his Family Crest (associated with Life) and on his Tombstone (associated with Death). Electrons and Positrons are polarized or as Niels Bohr is quoted, “Contraria sunt complementa” (Opposites are complementary). Perhaps the next Yin and Yang will be the Higgs Boson and the Anti-Higgs Boson. We shall see.

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