**Introduction**

Just as in other areas in the field of computer science, making the leap from classical- to quantum-mechanical properties as a basis for software developments introduces an entirely new level of possibility for real-world applications. For example, the basic implications of the concept of the qubit alone are enormous: the possibility of ultra-fast communications, up to the speed of light, as well as the potential availability of coding based on higher-order numeric systems (quaternary, rather than binary information, for example).

The introduction of quantum-mechanical principles to the area of cryptography, likewise, creates the opportunity for immensely powerful encryption protocols. By using basic tenets of subatomic physics, such as the Uncertainty Principle and Bell’s Theorem, computational cryptographers now have the power to create what amount to essentially unbreakable codes. Previously, when classical encryption methods relied on the increasing complexity of mathematical functions, there always existed the threat of an enemy with a more powerful computer able to intercept decipher an encrypted transmission. However, no computer, no matter how strong, is able to simultaneously measure orthogonal quantum eigenstates or preempt the prediction of spin states between quantum-entangled particles. The universality of physical law, in effect, becomes a computational tool in quantum cryptography.

In this project, we will investigate one of the most useful and fundamental processes of quantum cryptography: quantum key distribution (QKD), whereby two communicating parties establish a secret key through quantum-mechanical procedures. We will first examine, after a discussion on the underlying physical and mathematical concepts, the Bennett-Brassard Protocol, published in 1984, which uses polarized photons as transmitted qubits. Following this, we will discuss the other major protocol for quantum key distribution, the Eckert Protocol, published in 1991, which instead revolves around measuring the spin of entangled particles. The project will conclude with a brief discussion of the current development of QKD, including recent experiments and new directions for research.

**Key Terms**

*quantum channel* – a path through which quantum information can be transported; in quantum computing this is most often a fiber optic cable that transports photons

classical channel – any form of communication between two parties that does not rely on quantum-mechanical principles

*qubit* – a unit of information (a binary bit, 0 or 1) which has been encoded in the quantum property of a particle, such as the spin of an electron or the polarization of a photon

*Alice* – a term for the sending party across a communication channel

*Bob* – the receiving party of an information transaction

*key* – a series of bits that is shared between Alice and Bob in order to establish the security of their communication channel; if the two parties can successfully match their secret key, then they know that their communications are secure

*Eve* – short for “eavesdropper,” a third-party hacker who attempts to intercept communications between Alice and Bob or otherwise compromise the security of their communications channel

*one-time pad* – an encryption method that combines every data point of a communicated message with a corresponding bit in a pre-established secret key; a key used for a one-time pad should be exactly as long as the message, and discarded and regenerated after every use. The name “one-time pad” refers to Cold War-era espionage, when spies would lay a pad of paper with a written cipher over a message to encrypt it, then destroying the pad.

**I. Quantum-mechanical Systems and Photon Polarization**

**II. The Bennett-Brassard Protocol**

**III. The Einstein-Podolsky-Rosen Paradox and Bell’s Theorem**

**IV. The Eckert Protocol**

**V. Experimental Applications of Quantum Key Distribution**

**References**

Bennett, C., F. Bessette, G. Brassard, L. Salvail and J. Smolin, “Experimental Quantum Cryptography,” *Journal of Cryptography*, Vol. 4, no. 3, 1992, pp. 3-28.

Bennett, C.H. And G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” *Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing,* Bangalore, India, December 1984, pp. 175-179.

Eckert, A, “Quantum cryptography based on Bell’s theorem,” *Physical Review Letters*, Vol. 67, no. 6, 5 August 1991, pp. 661-663.

Goswami, A., *Quantum Mechanics*, Second Edition, 2003, Waveland Pr Inc.

Griffiths, D.J., *Introduction to Quantum Mechanics*, 1995, Prentice Hall, Inc.