Quantum Communication Protocols in a Topological Fashion
Quantum communication protocols; Topological Quantum Field Theory (TQFT); Chern-Simons Theory; Jones Polynomial
From all intriguing phenomena in quantum mechanics, entanglement is perhaps one of the most profound and fundamental. This strange property that emerges from the composition of Hilbert spaces and consists purely of quantum correlations, opened the doors for a plethora of applications and remains as a fundamental concept for connecting diverse fields of physics. Among its remarkable applications are quantum communication protocols, such as quantum teleportation, entanglement swapping and quantum erasure correction. In this work, we explore how Topological Quantum Field Theories (TQFT's) can provide a visual interpretation of these protocols, highlighting a connection between quantum entanglement, Chern-Simons theory and a topological invariant of knots, the Jones Polynomial.