Boua 1
Quantum Entanglement: Technology of the Future
Jane-Valeriane Kimberly Boua
A Review of the theories of Quantum Mechanics
Math 89S Duke University
January 2016
Introduction
Quantum mechanics is rooted in theories developed by Max Planck and his solution to black body radiation as well as Albert Einstein’s explanation of the photo electric effect that won them both Nobel Prizes. Quantum Theory began when scientist Robert Hooke and Leonhard Eulerproposed the wave properties of light (Coolman, 2014).Quantum mechanics is the study of the behavior of matter, and the attractions of energy at the atomic and subatomic levels. Quantum physics states that an unobserved atom exists in all possible states, but when observed or measured,it exists in one state (Carson, 2000).Hence,Quantum entanglement describes a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently. Measurements are performed on particles, using dimensions such as position, momentum, spin, and polarization, and when the particles are entangled, they are found to be correlated (Coolman 2014).
The Copenhagen Interpretation
The Copenhagen interpretation was devised from1925 to 1927 (Carson, 2000). The idea suggest that physical systems cannot have definite properties prior to being measured; the quantum mechanics of a system can only be predicted using probabilities that the measurements will produce certain results (Carson, 2000). Also, the interpretation suggestsa set of principals on which Quantum physics should be based on (Howard, 2004).Many people have objected the Copenhagen interpretation. According to John G. Cramer, a professor of physics at the University of Washington and opponent of the Copenhagen interpretation, “Despite an extensive literature which refers to, discusses, and criticizes the Copenhagen interpretation of quantum mechanics, nowhere does there seem to be any concise statement which define the full Copenhagen interpretation.” (Cramer,1986).
The term originated from Werner Heisenberg who had been an assistant to Niels Bohr at his institute in Copenhagen duringthe 1920’s (Carson, 2000). The term originated for a set series of lectures given by Heisenberg. The interpretation is very informal in the sense that there is no formal text that describes exactly what the Copenhagen interpretation is, rather it is a concept (Howard, 2004).
Schrödinger’s Cat
Schrödinger’s Cat was a thought experiment that highlighted issues related to the Copenhagen Interpretation. The Copenhagen Interpretation says that systems cannot have definite properties prior to being measured and exists in all states (Carson, 2000). Erwin Schrödinger theorized the state of a cat using the principles predicted by the Copenhagen interpretation to demonstrate what was inherently wrong with quantum superposition. Schrödinger had the reader imagine a cat inside a container with a Geiger counter (which measures ionizing radiation), radioactive material, poison, and a hammer (Schrödinger, 1935). If the Geiger counter detected radiation, the hammer would swing down and break the vile of poison, killing the cat (Schrödinger, 1935). It would be impossible to predict the state of the cat unless someone opened the box and observed the cat, therefore the cat would be simultaneously dead and alive, which could not be true, because it is impossible for an organism to exists as both dead and alive (Schrödinger, 1935). Schrodinger argued that there must be some other explanation to explain quantum theory because the theories suggested by the Copenhagen Interpretation cannot exists (Schrödinger, 1935).
The EPR Paradox
The EPR paradox was a thought experiment between Einstein and his colleagues, Boris Podolsky and Nathan Rosen based on the Copenhagen interpretation that claimed to show that the wave function proposed by Louis de Broglie and Erwin Schrödinger does not provide a complete description of physical reality, and hence the Copenhagen interpretation was unsatisfactory (Einstein, Podolsky, Rosen 1935). They attributed some of the uncertainty in that is inherent in quantum mechanics to “Hidden variables”(Einstein, Podolsky, Rosen 1935).
It has been suggested that once two atoms, for example, become entangled in a way thatthey can be described by a single wave function,andonce they have separated, they can still be described by this single wave function, even at infinite distances (Carson, 2000).In effect, measuring one will determine the state of the other. It was known from prior experiments, specifically the half-silvered mirror experiments, that once one quantity was measured, for example, the spin around the axis of an atom, the conjugated quantity became indeterminate. The explanation for this effect at the time was the Heisenberg’suncertainty principal. The goal of the EPR paper was to show that this explanation was inadequate. The paper referred to two particles, A and B and showed that measuring A will cause B to become undetermined even if there was no contact(Einstein, Podolsky, Rosen 1935). It showed that the dimensions of each particle were mutually exclusive.Theories suggested by Copenhagen Interpretation contradict Albert Einstein’s Theory of General Relativity in that it suggests information can move faster than the speed of light, while the Theory of General Relativity suggest that no information can move faster than the speed of light.
Bell’s Theorem
Bell’s Theorem widely contradicted the EPR paradox in that in stated, “No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.” (Bell, Alain 1972). John Stewart Bell devised an experiment that proved that “spooky action” did indeed exist (Schneider, 2005). Spooky action was a term coined by Albert Einstein in his paper regarding the EPR paradox to describe the idea that quantum entangled atoms cannotexist because they violate the general theory of relativity(Einstein, Podolsky, Rosen 1935). A Bell test experiment is designed to test whether or not the world operates using local hidden variables or by the quantum entanglement theory of quantum mechanics (Schneider, 2005). In laymen’s terms, once atoms become entangled, the behavior of one should automatically predict the behavior of the other. The test rules out hidden variables that can be attributed to spooky action (Bell, Alain 1972). Although the test successfully ruled out local hidden variables, the test still did contain loopholes(Schneider, 2005).
There are two main types of Bell test, a CH74 test and a CHSH test (Thompson). In the CH74 test, named after Clauser and Horn operated in a way that the source produced a pair of photons, each sent in the opposite direction. Each photon will encounter a polarizer whose orientation is set by the experimenter (Thompson). The signals are detected and coincidences are counted using a coincidence monitor. A coincidence is the number of times the photons are measured in the same way that their spins are accurately predicted. According to quantum theory, if the two photons have the same wave function, the measurement of one photon affects the other instantaneously (Carson, 2000). Local realism states that the measurement of one photon has no influence whatsoever on the other. A CHSH test operates using the same principles except that in a CHSH test where the photons reach polarizers set at angles a or b. Once the photons hit the polarizers, they exit as either positive or negative (Thompson). If the signals reach the two side of the coincidence monitor CM within a preset time window they are registered as a coincidence (Thompson).
Figure 2. Single Channel Bell Test
Figure 3. Two Channel Bell Test
Delft University in the Netherlands created a Loop-Hole free bell test in which all loopholes were simultaneously closed (Loop-hole free test). In 2015, The Hanson loophole free bell test simultaneously addressed the detection loophole, the locality loophole and the memory loophole. The detection loophole is where the detection efficiency is under 100%. The ability to accurately predict the behavior of the other atom, was under 100% prior to experiments that closed this loop hole. The memory loophole occurs when the same measurement occurs at the same photon repeatedly.Again in 2015, a loophole free bell test was created that used photons.Prior experiments including The Geneva 1998 Bell test which showed that distance of about 10 kmdid not destroy the entanglement of photons.
Quantum Cryptography
A practical application of the theories of quantum entanglement include quantum cryptography. Quantum cryptography was proposed by Stephen Wiesner who introduced the concept of quantum conjugate encoding (Bennett, Giles 2014). The more popular forms of Quantum cryptography include public key encryption and signature schemes. Public Key cryptography is a process in which a message is mixed in a way that people who are not intended to read a message are unable to do so. The benefit of using quantum cryptography is that there is no way that the information being sent or received can be tampered with. The act of reading data encoding in the quantum state changes the state (Bennett, Giles 2014).
The most applicable and developed use of quantum cryptography is quantum key distribution(Bennett, Giles 2014). This guarantees fast, secure communication. An important tool is the ability of the two communicating individuals, in this case, Alice is traditionally referred to as the sender, and Bob as the receiver, to detect the presence of a third party, traditionally referred to as Eve. This idea is set on the principal of quantum mechanics which states that the process of measuring a system in the quantum state disrupts the system (Carson, 2000). Thus, using quantum key distribution, the presence of a third party can be detected. In this system, two parties create a secret key,and only the two of them know which is used to communicate messages. Public key encryption is currently based on mathematical computations and does not provide the amount of secrecy as does quantum key distribution(Bennett, Giles 2014). Communication uses information encoded into quantum states called qubits. Photons are generally used for these operations.
BB84 and E91 Protocol
BB84 protocol is a system that uses photon polarization states to transmit information(Bennett, Giles 2014). It was the first quantum cryptography tool of its kind. In general, Alice and Bob are connected via a quantum communication channel or free space. The BB84 system begins with Alice sending a key to Bob over a public quantum channel. Bob receives that key and is able to decipher the key as well as any interruptions in communication as a result of Eve. Once Bob receives the key, there are three possible states, between all three individuals, Alice’s, Bob’s and Eve’s. In effect, since only Alice knows the initial key, it is impossible for Bob or Eve to distinguish between the states of the qubits(Bennett, Giles 2014).
The E91 protocol or Ekert scheme also uses entangled pairs of photons based on Bell’s Theorem (Ekert, 1991).They can be created by Alice, Bob or from an outside source, like eavesdropper Eve(Ekert, 1991). The photons are distributed in a way that each individual ends up with a pair. This process relies on two properties of entanglement(Ekert, 1991). The photons are perfectly correlated in a way that Alice and Bob have identical polarizations. The two communicating parties, Alice and Bob, will have perfectly synchronized polarizations, however the polarizations are completely random, it is impossible for Alice or Bob to predict the orientation of the polarization(Ekert, 1991). Any attempt to destroy these correlations by Eve will be detected by both Bob and Alice (Ekert, 1991). There are privacy protocols built in so that Alice, the receiver can measure photons she receives to determine whether or not there is interference, or the presence of an eavesdropper, Eve(Ekert, 1991). One major problem associated with Quantum Key Distributions is that the maximum distance they have been known to travel over is 143 kilometers (Ma, 2012).
The Future of Quantum Cryptography
The future of quantum cryptography and quantum entanglement are very bright. Microsoft and other organizations have been discussing the possibility of the release of a quantum computer within the next ten years (Brandom, 2015). More research is being done on the future of quantum entanglement and hopefully more progress will be done on the distance in which information is travelled as opposed to the maximum 143 kilometers that has been scientifically studied (Ma, 2012). Once the distance barrier is solved, then more opportunities open up for quantum entanglement.
Conclusion
Quantum Mechanics was born from a number of different scientist and challenged many of the ideas classical physics. The Copenhagen Interpretation provided an interesting interpretation on how quantum mechanics should be operate. This was widely unpopular among many renowned scientists of the time, including Einstein himself. Einstein and some of his fellow colleagues, Podolsky and Rosen released the EPR paper, which ascertained that the theory of quantum entanglement was due to local hidden variable and it was in this article that Einstein coined the term “spooky action”. Spooky action is the contradiction between quantum entanglement and the theory of general relativity in that it predicts that information can travel faster than the speed of light. J.S. Bell released a theorem in which he supplied a test that proves that quantum entanglement is not due to local hidden variables. The theorem did have many loopholes until recently Delft University in the Netherlands managed to close all of these loopholes. A lot of progress has been made in the field of quantum entanglement, although a lot has to get done.
Work Cited
Bell, J. S., and Alain Aspect. "Speakable and Unspeakable in Quantum Mechanics." Speakable and Unspeakable in Quantum Mechanics Collected Papers on Quantum Philosophy: 169-72. Web.
Bennett, Charles H., and Gilles Brassard. "Quantum Cryptography: Public Key Distribution and Coin Tossing." Theoretical Computer Science 560 (2014): 7-11. Web. 14 Feb. 2016.
Brandon, Russel. "Microsoft Lab Predicts a Working Quantum Computer within 10 Years." The Verge. Vox Media, 15 Oct. 2015. Web. 21 Feb. 2016.
Carson, Cathryn. "The Orgins of the Quantum Theory." Beam Line 30.2 (2000): 6-19. Web. 12 Feb. 2016.
Clauser, J. F., and A. Shimony. "Bell's Theorem. Experimental Tests and Implications." Rep. Prog. Phys. Reports on Progress in Physics 41.12 (1978): 1881-927. Web.
Communication, Webredarticle. "Loophole-free Bell Test TU Delft Crowns 80-years-old Debate on Nature of Reality: Einsteins." Delft University of Technology. Web. 13 Feb. 2016.
Coolman, Robert. "What Is Quantum Mechanics?" LiveScience. TechMedia Network, 26 Sept. 2014. Web. 10 Feb. 2016.
Cramer, John G. "Transactional Interpretation of Quantum Mechanics." Compendium of Quantum Physics (2009): 795-98. Web. 12 Feb. 2016.
Einstein, A., B. Podolsky, and N. Rosen. "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Phys. Rev. Physical Review 47.10 (1935): 777-80. Web.
Ekert, Artur K. "Quantum Cryptography Based on Bell’s Theorem." Phys. Rev. Lett. Physical Review Letters 67.6 (1991): 661-63. Web. 14 Feb. 2016.
Howard, Don. "Who Invented the “Copenhagen Interpretation”? A Study in Mythology." Philosophy of Science 71.5 (2004): 669-82. Web.
Ma, Xiao-Song, Thomas Herbst, Thomas Scheidl, Daqing Wang, Sebastian Kropatschek, William Naylor, Bernhard Wittmann, Alexandra Mech, Johannes Kofler, Elena Anisimova, Vadim Makarov, Thomas Jennewein, Rupert Ursin, and Anton Zeilinger. "Quantum Teleportation over 143 Kilometres Using Active Feed-forward." Nature 489.7415 (2012): 269-73. Web. 12 Feb. 2016.
Schneider, David R. "Bell's Theorem with Easy Math." Bell's Theorem with Easy Math. Dr. Chinese, 2005. Web.
Schrödinger, Erwin. "Die Gegenwärtige Situation in Der Quantenmechanik (1935)." Die Deutungen Der Quantentheorie (1984): 98-129. Web. Translation. John D. Trimmer
Thompson, Caroline H. "Introduction." The CH74 Bell Test. Web. 11 Feb. 2016.
Tretkoff, Ernie. "This Month in Physics History.": Einstein and the EPR Paradox. American Physical Society. Web. 15 Feb. 2016.