Quantum Science Philippines
Quantum Science Philippines

A Summary of Decoherence and the Transition from Quantum to Classical by Wojciech H. Zurek

Normie Jean B. Sajor

Quantum mechanics is one of the most functional theories in the world of physics.  It describes the workings of particles, atoms, and molecules with extraordinary accuracy and also explains the action of lasers and transistors. Yet, the debate about the relation of quantum mechanics to the familiar physical world continues.

For instance, the so-called measurement problem has been a source of continual speculation. In quantum mechanics, it is the unresolved problem of how the wavefunction collapses. The wavefunction obeys the deterministic Schrödinger equation into a linear superposition of different states. However, actual measurements always find the physical system in a definite state. But why we cannot predict precise results for measurements, but only probabilities?

The Copenhagen interpretation which is proposed by Niels Bohr was the first accepted explanation of how a single outcome emerges from the many possibilities and insisted that a classical apparatus is necessary to carry out measurements.  It created a dividing line between classical and quantum. The border line must be mobile according to Niels Bohr. Classical is identified frequently as macroscopic but the insufficiency of this approach has become visible as a result of recent developments such as the cryogenic version of the Weber bar, a gravity wave detector which must be treated as a quantum harmonic oscillator even though it can weigh a ton.

There might be no boundary between classical and quantum since macroscopic systems cannot always be safely placed on the classical side of the boundary. The many-worlds interpretation claims to do away with the boundary. In this interpretation, the superpositions evolve without end according to the Schrodinger equation. Zurek stated that “Each time a suitable interaction takes place between any two quantum systems, the wavefunction of the universe splits, so that it develops ever more branches.” Hugh Everett, the author, proposed the idea that the wavefunction never collapses. The many-worlds interpretation and other post-Everett interpretations use decoherence to explain the process of measurement or wavefunction collapse.

Decoherence try to clarify the transition from quantum to classical by analyzing the interaction of a system with a measuring device or with the environment. It can be viewed as the loss of information from a system into the environment. As Stahlke said, “any interaction with the environment leads to an entanglement between the particle’s state and the environment’s state. As the entanglement diffuses throughout the environment the total state can no longer be separated into the direct product of a particle state and an environment state.”

Although decoherence does not give the solution in the measurement problem but it does bring some enlightenment. It is still unknown at which point the wave actually collapses and caught the attention of the scientific world. Environmental entanglement provides a mechanism in which wave collapse can transmit into the system from distant.

[1.] Zurek, Wojciech H. Decoherence and the Transition from Quantum to Classical. Physics Today. October,1991.

[2.] Stahlke, Dan. Quantum Decoherence and the Measurement Problem

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Advances in Quantum Computing

Catherine Therese J. Quiñones

For many years, computers have doubled in power every year or so, as what Moore’s law predicts. This means that transistors are getting smaller and smaller and will eventually approach the size of an atom. However, in the atomic regime, the physics is completely different from what is observed in the electronic devices of today. In this level we have to consider the strange effects of quantum mechanics (QM).

In the classical model of a computer, the most fundamental building block of information, the bit, can only exist in one of two distinct states, a 0 or a 1 encoded in electronic components such as transistors. A bit is analogous to a head and a tail of a coin. When you toss a coin you can only have one of the two states. However, for a quantum computer, a quantum bit or a ‘qubit’ does not follow these rules. A qubit can be 0 or 1 or 0-1 or 0+1 or 0 and 1, all at the same time! This is where quantum mechanics comes in, i.e., the principle of superposition of states. Such superposition of states can lead to a simultaneous processing of 2N values that are being expressed simultaneously by N qubits. This allows far greater flexibility than the binary system. This means that more qubits you have, more options you can work with, thus, the faster you go.

We may now ask, What is the best way of creating a quantum computer or giving a system a qubit form? Physically, qubits are encoded in ions, photons, atoms/molecules, or electrons. Different qubit systems have its advantages and disadvantages. For instance, charged particle or ion trapped within an electromagnetic field or trapped using optical techniques can serve as a qubit however it is vulnerable from decoherence. It is very much important for a quantum computer to isolate the qubit because any interactions from the environment destroy the superposition of states thus causing decoherence or loss of its quantum character. Now, for a molecule, the up and down directions of the nuclear spin can also act as a qubit. Nuclear spins make excellent quantum memory since they interact with their environment only via their tiny magnetic fields. However, for the same reason, this makes the quantum information hard to access. On the other hand, photons can also be fast and robust carriers of quantum states encoded in polarization state thus making them a good medium by which to transmit quantum information. However, these attributes also mean that they are difficult to localized and store. Another approach is by using a solid state device, either a qubit achieved by a superconducting circuit using the Josephson junction or a qubit achieved by a semiconductor quantum dot. Quantum bits encoded in states with different electrical charges can be manipulated and measured very rapidly but the charges make short-lived qubits since they are strongly coupled to their local electrical environment.

Another problem with quantum computing is that if you observe or measure the quantum state of a qubit, it changes its value. So scientists must devise an indirect method of determining the state of a qubit, that is, by taking advantage of another quantum property called “entanglement.” At the quantum level, if you apply a force to two particles they become “entangled” meaning, a change in the state of one particle is instantly reflected in the other particle’s change to the opposite state. So by observing the state of the second particle, physicists hope to determine the state of the first. Thus, quantum effects can be used to acquire information about the system.

A working quantum computer should contain thousands of qubits in order to solve real-world problems usefully. One must have a technology that enables quantum systems to exist as coherent states for a long period of time. Various methods are being experimented and give promising results. One solution is to use a hybrid approach known as quantum network to maximize the different qubit systems. Basically, this approach involves the transfer of quantum information from one qubit form to another. For instance, quantum states which are stored and manipulated in matter qubits are mapped into photons for long distance transmission. The challenge now is to develop techniques in order to coherently morph quantum bits from matter to light.

So, what is the big deal with the quest for high speed computing and quantum computation? Actually, Mother Nature has endowed us with physical phenomenons which are way way too far complicated to solve using conventional computing. For example, we may want to know the ground state of a particular homogeneous system, such as an array of mutually coupled identical spins, or measure simple correlations between different parts of the system. This will pave the way to understanding condensed-matter systems and understanding of materials such as high-temperature superconductors. Not only that, by using algorithms such as Shor’s algorithm, a quantum computer would be able to crack codes much more quickly than any ordinary computer could. Breaking such encryption standards can however put one’s security at risk. Another breakthrough if quantum computing would be a success is the creation of computers that would be capable of simulating conscious rational thought – the key to achieving true artificial intelligence.

As of now, baby steps were made towards the goal of large scale quantum computers. The future of quantum computing is very promising but the benefits must outweigh the risks it could bring.

About the author:

Catherine Therese J. Quiñones is a physics graduate student of Mindanao State University – Iligan Institute of Technology (MSU-IIT). She is currently doing research in the field of medical physics. Her research interests also include high energy physics and astroparticle physics. ☆

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Quantum Entanglement towards scalable Quantum Computing

Gibson T. Maglasang

Quantum Physics, quantum information science and quantum computing are among the growing field of science and crowning intellectual achievements over the past century. Basically, it involves the storage, manipulation, teleportation and communication of information in quantum systems where great enhancements are possible due to entanglement. In this article, entanglement of a two fixed single-atom is demonstrated thru experiment. Moreover, the state of each of the two remotely located ion separated by one meter is measured in the unrotated and rotated by basis in order for the entanglement can be verified.

At the start of the experiment, each Ytterbium ion is trapped, laser cooled and initialized at the ground state [eq]|0 0\rangle[/eq]. Immediately then, the two ions are simultaneously excited by a 2-ps [eq]\sigma[/eq] polarized laser pulse to ensure that each ion emits at most a single photon. In addition, this process prepares the ion in the excited state with an excitation probability of [eq]P_{exc}=0.5[/eq]. The excited particle falls back to the one [eq]\left(|1-1\rangle\right)[/eq] or the other two qubit ground states [eq]\left(|10\rangle[/eq] or [eq]|\uparrow\rangle[/eq] and [eq]|00\rangle[/eq] or [eq]|\downarrow\rangle)[/eq] thereby emitting [eq]\pi[/eq]-polarized photon and [eq]\sigma[/eq]-polarized photon respectively. Each ion emits a photon whose frequency is perfectly correlated with the two atomic qubit states. It is then the atomic qubit and photon entanglement that will directly predict the entanglement of atoms. The spontaneously emitted photon from each ion are collected by the lenses, routed to the fiber-optic cable. It is further carried out to a 50-50 beam splitter where photons pass straight through the splitter or be reflected each with equal probability. Photons emerging from the splitter are then sent to a beam polarizer to filter out the [eq]\pi[/eq] decay channel. Simultaneous detection from both detectors (PMT) occurs only if the photons are in the antisymmetric state. Thus, revealing the odd parity wavefunction in the ion-ion entangled state [eq]\left(|\Psi\rangle_{atom}=|\uparrow\rangle_a|\downarrow\rangle_b-|\downarrow\rangle_a|\uparrow\rangle_b\right)[/eq].

Thus, a successful quantum entanglement between two remotely located ions is portrayed and such a network of remotely entangled ions or atoms could be of immense help towards scalable quantum computation and communication.

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Brief history of the development of quantum mechanics

Karl Patrick S. Casas

Any object of higher temperature than its surroundings radiates and loses heat. More radiation is produced if you raise the temperature even higher. Even objects at room temperature glow, but in the form of infrared radiation, which is not detectable by the eye. A black body absorbs all frequencies and emits larger quantities of some wavelength. In 1900, Max Planck invented a function that explained the spectrum at all frequencies. He later interpreted his law: the electromagnetic field can absorb and emit electromagnetic radiation only in integer multiples of a fundamental unit of energy equal to Planck’s constant multiplied by the frequency. This discovery marks the start of the old quantum theory. The ideas in classical mechanics were assumed to hold but with the additional assumption that only certain values of a physical quantity is allowed.

In 1905, Albert Einstein proposes that light, which has wave-like properties, also consists of discrete, quantized bundles of energy called photons. This theory explained the photoelectric mystery. Niels Bohr, in 1913, combined the postulates of Planck and Einstein to build characteristic discrete energy states that atoms should possess. These results accounted for the series of lines observed in the spectrum of light emitted by atomic hydrogen. Arnold Sommerfield added Bohr’s principal quantum number n with orbital quantum number l and angular quantum number m. As a consequence, the Bohr-Sommerfield theory could explain the stark effect and the normal Zeeman Effect but failed to explain outstanding problems such as the helium problem and the anomalous Zeeman Effect.

In around 1924, due to unexplained results and anomalies, it became clear that the old quantum physics was not the whole story. In 1925, Werner Heisenberg, together with Max Born and Pascual Jordan developed a complete theory of quantum mechanics called “Matrix Mechanics”. Each parameter of classical mechanics can be assigned a corresponding matrix in quantum mechanics. In that same year, Wolfgang Pauli formulates the exclusion principle of electrons in an atom.

Going back in 1923, Louis de Broglie proposed his “Wave Nature of Matter”. Particles of matter have dual nature and in some situations act like waves. This idea is developed into a new formulation of quantum mechanics by a German Edwin Schrodinger. He became famous of his Schrodinger equation that views orbiting electrons as matter waves. Schrodinger’s interpretation of the wavefunction [eq]\psi[/eq] as the density distribution was wrong and it was Max Born who figured out the statistical meaning of [eq]|\psi|^{2}[/eq] as the probability density. In Born’s interpretation, if something is observe it will be a whole electron unlike Schrodinger’s idea that a small fraction of an electron will be detected there.

These two competing versions of new quantum physics were on debate over which one was correct. It was soon shown that Schrodinger’s formulation and Heisenberg’s formulation are equivalent.

In 1925, Wolfgang Pauli had inferred from the laws in the Periodic System of the elements the well-known principle that a particular quantum state can at all times be occupied by only a single electron. Pauli’s exclusion, in 1926, gave birth to the discovery of the fourth quantum number, electron spin s, by Samuel Goudsmit and George Uhlenbeck which has only two quantized values. In that same year, Paul Dirac extended the theory to relativistic and field-theoretic situations. In 1927, Heisenberg formulates the uncertainty principle in which the more precisely one property is known, the less precisely the other can be measured.

The differences of Quantum Mechanics and Classical Physics became clear. Classical world is deterministic, that is, future can be predicted by using known laws of force and Newton’s laws of motion. In the quantum world, it is impossible to know position and velocity with certainty. Only probability of future state can be predicted using known laws of force and equations of quantum mechanics.

About the author. Karl Patrick S. Casas is a graduate student in Mindanao State University- Iligan Institute of Technology, Iligan City, Philippines. He hopes to finish his master’s degree as soon as possible.

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Total Spin States of a Two Particle System Measured at the Ground State

Christine Marie Ceblano, Liza Marie Dangkulos, Lutchie Dyan Mendoza and Normie Jean Sajor

Spin in particle physics and quantum mechanics is a fundamental characteristic property of elementary particles, composite particles and atomic nuclei. All elementary particles of a given kind have the same spin quantum number which is an important part of a particle’s quantum state.

The principal spin quantum number s is given by                                                          f1

where n = 0, 1, 2, 3, … can be any non- negative integer.

Quantum mechanical spin also contains information about direction. Quantum mechanics states that the component of angular momentum measured along any direction (along  z – axis) is

f2

where s is the principal spin quantum number.

One can see that there are 2s + 1 possible values where 2s + 1 is the multiplicity of the spin system. This multiplicity corresponds to quantum states in which the spin is pointing in the +z or −z directions.

For an instance, there is a 2-particle system at the ground state. The first particle has spin 2 and the second has a spin 3/2 . That is,

f3

In order to find the total spin states which are available to this system, the multiplicity of the spin system must be obtained.

For particle 1 where s1 = 2, the multiplicity is 2s + 1 = 2(2) + 1 = 5 states.

For particle 2 where s2 = 3 /2 , the multiplicity is 2s + 1 = 2(3/2) + 1 = 4 states.

Thus, the 5 states of the first particle are −2,−1, 0, 1, 2 and the 4 states of the second particle are −3/2,−1/2 , 1/2 , 3/2 .

To have the total spin states, combine all the obtained states above by pairing each spin’s z– component.

Summarizing all the states, we have

f4

Given the same values (s1 = 2 and s2 = 3/2) and the particles spin’s z-component, one can get the possible total spin values as well as the probabilities of getting such values. The particle state |s m > with total spin’s and z-component m will be some linear combination of the composite states |s1 m1 > and |s2 m2 >.

f5

f7

Suppose that the spin’s z-components for the first and second particle are given to be 0 and 1/2 respectively, then  m1 = 0 and m2 = 1/2. The possible total spin and the corresponding probabilities can be found with the help of the Clebsch − Gordan coefficients’ table below.

clebsh_4colored_not stretched

f9

Looking at the table under the category 2 x 3/2 and with m1 = 0 and m2 = 1/2 (the highlighted row), one could get the total spin of 7/2 (with probability of 18/35), 5/2 (with probability of 3/35), 3/2 (with probability of 1/5) and 1/2 (with probability of 1/5).

Using the form in equation 3, we have

f10

As always, the sum of probabilities is 1 (the sum of the squares of the row highlighted in the Clebsch − Gordan table is 1), i.e.

f11

As a summary, there are 20 possible total spin states for this 2-particle system at the ground state. Then by using Clebsch−Gordan coefficient table, the possible values of the total spin and probabilities of getting such values are obtained.

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