My Work
Since its establishment in 1900, Quantum Mechanics (QM) has been one of the most successful theories ever, as it has passed every test and experiment founded in its complexity (Farmelo 2019). Additionally, Quantum Mechanics has given rise to a variety of concepts involving computing, atomic physics, and chemistry (Stone 2013),(Nielson and Chuang 2013). Quantum computation and quantum information are both built on a concept for particles known as a qubit, and are often described mathematically.(Nielson and Chuang 2013). These bodies of information are subject to many of the effects of quantum mechanics, giving them unique strengths when compared to classical information carriers. Two of the most important properties that affect this system of quantum bits are superposition and entanglement. (Nielson and Chuang 2013)
Taking advantage of the various properties of quantum mechanics, one experimental approach that is used in both quantum information science and quantum computing is the qubit. [1] In classical computing, a bit is a fundamental concept of information transfer, capable of holding two values, a 1 and a 0, or the presence or absence of charge respectively. (Nielson and Chuang 2013) A qubit can be visualized as a sphere (Figure 1), where each of its possible states is a point on the outside of the spherical shape, represented by Ѱ in Figure 1(Nielson and Chuang 2013). This is called a bloch sphere. States closer to the “downward most” pole of the sphere, as seen in Figure 1 where the 1 is located, have more energy than those above them. (Nielson and Chuang 2013). Due to the infinite number of points possible on the surface of the sphere, there are an infinite number of conceivable states that the qubit can be in, however the qubit must be unobserved. (Nielson and Chuang 2013). This combined “super-state” of all of the combined unobserved states is called a superposition, and is a composition of the possible states and each of their relative probabilities for the qubit. States closer to each pole have a variance in the probability of being measured in each respective pole value based on the position of the unmeasured value, which is determined by the square of the cosine of half the angle to the desired pole. (Lo 2003) Superposition allows the qubit to contain much more information than a classical bit. (Nielson and Chuang 2013). The act of observing or measuring a qubit causes all of the unobserved probability states to collapse and the value of the qubit is established as one concrete value, based on the probabilistic position of the point on the surface of the unobserved qubit’s sphere. . (Nielson and Chuang 2013).This value can be changed by adding or removing energy from the quantum system. (Nielson and Chuang 2013). Entanglement is another key advantage that qubits have over a classical bit. (Nielson and Chuang 2013). Entanglement allows multiple qubits to be connected to one another thus allowing them to achieve a higher number of possible information states in comparison to a classical system. (Nielson and Chuang 2013). The quantum effects of entanglement, which will be explained further, angered many of the founding scientists who created the basics of quantum mechanics, so much so that they wrote a paper protesting the idea’s need for revision. (Stone 2013). The 1935 EPR paper has been the basis of many experiments since its publication, and boldly claimed that entanglement, or Einstein’s “spooky action at a distance”, violated the theory of relativity. In many ways, Einstein was also upset about the way that quantum particles are subject to nonlocal realism, and the fact that these objects have no definite properties until measured by an observer. (Stone 2013). The argument claimed that the quantum effects of entanglement allowed information to propagate faster than the speed of light [3]. Theoretical physicist John Stewart Bell deduced a method, through an original thought experiment, to prove whether the accusations made in this publication were valid. (Bell 1964). Unfortunately, Bell was limited by the technology of his time and could not conduct the experiment himself. When the experiment was finally conducted with particle spins, one example of which was directed by Bohm, physicists found that entanglement did not allow particles to communicate, and that there were no hidden variables within the entangled objects as proposed (Bell 1964) Mathematically, Bell had opened up an entire world in quantum mechanics. The mathematical proof of his ideas, known as Bell’s inequality, is key to understanding the advantages that quantum mechanics can pose in relation to classical solutions. My research involves using these inequalities in simple games to test partial communication theories. Refer to the supplied explanatory video which outlines a classical version of one of these probability games. |